The bill seeks to revive the Prime Minister's plan to deport some asylum seekers to the east African nation - proposals ruled unlawful by the Supreme Court last year.
But a growing number of rebels have argued it does not go far enough and they want changes that will prevent legal challenges.
However MPs from the party's centre ground One Nation group are concerned that any hardening would risk breaking international law.
Rebel Tory MPs met at 5pm as they continue “urgent negotiations" on the changes.
Follow latest updates below...
19:29 , Rachael Burford
Junior Government aide Jane Stevenson has joined Lee Anderson and Brendan Clarke-Smith in resigning.
She was PPS in the Department for Business.
I have offered my resignation as a PPS this evening. I don't consider my votes to have been anti-Govt, but they do warrant resignation. In the Chamber earlier I paid tribute to @RishiSunak's work so far & welcomed his commitment made in Rome in Dec to lead talks on 🌍 frameworks
— Jane Stevenson MP (@Jane_Stevenson_) January 16, 2024
Numbers 'speak for themselves'
19:01 , Rachael Burford
Tory hardliner Mark Francois says "the numbers speak for themselves" when asked if he would vote against the Bill on Wednesday.
"I hope very much that the Government will listen and as a result of this... that the Government take stock and that perhaps there will be some possibility of tightening the Bill... tomorrow," he told Sky News.
"The numbers speak for themselves."
Vote on second Robert Jenrick amendment
18:51 , Rachael Burford
MPs are now voting on another amendment by former immigration minister Robert Jenrick, which aims to make it significantly harder for individual asylum seekers to challenge deportation orders.
Robert Jenrick's amendment fails
18:44 , Rachael Burford
MPs voted 525 to 58 against former Tory immigration minister Robert Jenrick's amendment, which was aimed at severely limiting individual asylum seekers' ability to appeal against being put on a flight to Rwanda.
60 Tory MPs rebel
18:34 , Rachael Burford
There were 60 Tory MPs who rebelled against the Government to support Sir Bill Cash's amendment.
These were 58 Conservatives voting against, as well as Miriam Cates and Sir Jacob Rees-Mogg who acted as tellers.
Scott Benton and Andrew Bridgen, who have been suspended by the Tory party and now sit as independents, also voted for the amendment along with eight DUP MPs.
Clause 2 passes
18:30 , Rachael Burford
MPs vote 331 to 262 in favour of clause two of the Bill, which states that Rwanda is treated as a safe country.
Rwanda legislation should be 'watertight'
18:29 , Rachael Burford
Lee Anderson and Brendan Clarke-Smith say they have consistently argued for the Government's Rwanda legislation to be watertight.
"It is therefore important in terms of credibility that we are consistent with this," they say in their resignation letter.
As deputy party chairmen they were bound by collective responsibility.
"It is with this in mind that we fully appreciate that whilst our main wish is to strengthen the legislation, this means that in order to vote for amendments we will therefore need to offer you our resignations from our roles," they add.
Responding to the resignations, Lib Dem MP Alistair Carmichael says: “Sunak’s Rwanda scheme just won’t work - and even the Deputy Chairmen of his own party know it.
“Rishi Sunak has yet again been embarrassed by his own MPs.
“If the Prime Minister can’t even settle squabbles in his own party, how can he be expected to run the country?"
'Safe country' clause
18:22 , Rachael Burford
MPs are voting on whether clause 2, which says Rwanda should be treated as a safe country for deportations, should remain in the Bill.
Sir Bill Cash's amendment fails
18:14 , Rachael Burford
MPs voted 529 to 68 to reject Tory MP Sir Bill Cash's amendment, which aimed to ensure UK and international law cannot be used to prevent people being deported to Rwanda.
Joint resignation statement
18:09 , Rachael Burford
Lee Anderson and Brendan Clarke-Smith have issued a joint resignation letter as they prepare to support Sir Bill Cash's amendment, being voted on now.
Cash's amendment will add a “notwithstanding clause” to the Bill, which would allow the Government to go ahead with deportations to Rwanda regardless of what the European Convention on Human Rights says.
My letter regarding tonight’s amendments. pic.twitter.com/EyneeRy4B9
— Brendan Clarke-Smith MP (@Bren4Bassetlaw) January 16, 2024
Tory deputy chairmen resign
18:00 , Rachael Burford
Lee Anderson and Brendan Clarke-Smith have resigned as Conservative Party deputy chairmen as they back the rightwing rebel amendments to the Bill.
SNP amendment fails
17:53 , Rachael Burford
The SNP amendment fails with 66 votes for and 337 against.
17:52 , Rachael Burford
MPs have begun voting on the first amendment, which is the SNP's saying the bill should declare Rwanda unsafe, instead of safe.
Rwanda is 'safe country'
17:39 , Rachael Burford
Immigration minister Michael Tomlinson says Rwanda is now a safe country.
The minister says the UK's new legally binding treaty with the Government of Rwanda "does in fact respond to the concerns set out by the Supreme Court".
Intervening, SNP MP Patrick Grady asks: "If then Rwanda is a safe and secure place in which asylum seekers can live comfortable and productive lives, why should the prospect of being sent there be a deterrent?"
Mr Tomlinson replies: "The deterrent is because those are seeking to come to this country and not to the country of Rwanda."
17:32 , Rachael Burford
Conservative MP Jane Stevenson, a Parliamentary Private Secretary in the Department for Business, confirms she is supporting rebel amendments to the Rwanda Bill.
She tells the Commons: "I want it to be as robust as it possibly can be because we need it to be fit for the crisis that we face.
"It is a crisis and my constituents certainly want to see results on that crisis, so I will support these amendments."
Ex Tory minister 'will vote against Bill'
17:30 , Rachael Burford
Sir Simon Clarke says he will vote against the Rwanda Bill if amendments are not made.
The ex Tory cabinet minister says: "The Prime Minister has said he will do whatever it takes.
"Unfortunately, I do not believe that as of this moment we are set to do whatever it takes to stop this problem.
"And I can only vote for this legislation if I believe genuinely and sincerely that it will resolve the problem."
Rebel Tories gather to discuss votes
17:17 , Rachael Burford
Dozens of Tory MPs have gathered for a meeting in Parliament to discuss the Rwanda plan.
They include former Prime Minister Liz Truss, ex Home Secretary Suella Braverman and Iain Duncan Smith.
New Conservatives co-chairman Danny Kruger, and former ministers Jacob Rees-Mogg and Simon Clarke are also present.
Government has 'not succeeded' in tackling immigration, says senior Tory
17:00 , Rachael Burford
Former cabinet minister Sir Simon Clarke tells MPs "this is our last chance to act in this Parliament".
He acknowledges the Government has "not succeeded" to address issues related to immigration despite trying on "multiple occasions" to do so.
He said: "It comes really down to the fundamental question of in whose interests do we sit here and do we legislate today? It's clearly, of course, the public interest.
"And I warned during the debates on Brexit - which I had hoped were relegated now to the annals of history - that this House was playing with fire if mainstream democratic politicians do not or cannot resolve the problems which face this country, our political process will I'm afraid move inextricably to the extremes.
"We've heard a lot of rhetoric, and it is rhetoric, from the Opposition benches about how extreme the position that we are advocating is.
"Trust me, it will be as nothing compared to who will sit on these benches if we fail in our task because we are at the limits of the tenable when it comes to the feelings of the British public."
Rebel amendments vote within hour
16:50 , Rachael Burford
MPs expect to vote on the Tory rebel amendments within the hour.
As a reminder, dozens of MPs on the right of the Conservative Party are supporting changes that they believe will beef up the Rwanda Bill.
The amendments are aimed at stopping interference by international courts in Government attempts to deport asylum-seekers to the African nation.
Critics argue the changes would breach international law.
These are the MPs who have backed the amendments:
Rishi Sunak still aims to have flights running to Rwanda by spring
16:20 , Rachael Burford
Rishi Sunak still aims to have flights taking off to Rwanda by the spring, Downing Street has said.
It comes despite plans to draft in more judges to speed up migrant appeals not set to be completed until summer.
Asked whether it was still the plan to revive the stalled scheme by spring, the Prime Minister's official spokesman said: "It is."
Number 10 reiterated that it will "listen if people want to put forward a legal position as relates to their amendments" but that it was working within "specific parameters and one of those is not collapsing the Bill".
Lady Chief Justice: 'Judiciary decides how judges are deployed'
15:43 , Rachael Burford
The country's most senior judge says decisions on how judges are deployed are "exclusively a matter for the judiciary".
The Lady Chief Justice, the first woman to hold the job, is appearing before the Commons Justice Committee.
Dame Sue Carr's comments come after the Government announced plans to draft in judges and free up courtrooms to speed up migrant appeals.
Asked about the practical implications of the move, Lady Carr said headlines about the plans draw "matters of judicial responsibility into the political arena."
She tells MPs: "Parliament has legislated, we - the judiciary - have acted in preparation for that legislation.
"But to be absolutely clear, matters of deployment of judges, the allocation of work for judges, and the use of courtrooms, is exclusively a matter for the judiciary, and more specifically, a matter for myself and the senior president of the tribunals. And it's really important that people understand that clear division."
Rebel Tory calls for Government to bring its own amendments
15:27 , Rachael Burford
Sir Bill Cash has suggested the Government brings forward its own amendments to the Rwanda Bill.
The veteran Tory help draft the controversial amendments being backed by rightwing MPs.
He tells the Commons: "I strongly urge the Government to note the sheer anger and frustration demonstrated in opinion polls and public concern that we get this Bill right and make it work.
"If not, this anger will continue up to and including the general election.
"Would it not be wise for the Government to reflect on the position, and that it would be better and wiser to come forward with their own amendments and use our majority, in line with our manifesto, granted to us by the general election in 2019, and in the national interest, and for the sake of all Conservative Members of Parliament whose seats will be so at risk if we do not do so?"
Charity urges MPs to vote down 'brutal' Rwanda Bill
14:56 , Rachael Burford
Safe Passage, a charity which helps unaccompanied children to reunite with family, has urged MPs to voted against the Rwanda Bill. Katie Morrison, CEO at Safe Passage said: “This Government must abandon its brutal tactics to banish refugees, not make the Rwanda Bill even more damaging by undermining the international and UK human rights laws that protect us all.
“At the very heart of this cruel policy are people who are simply seeking a safe life with their families, having fled war and persecution. The reality is, this Government has shamefully chosen to deny refugees safe ways to reach the UK to ask for protection, yet it’s determined to punish people whose only option is to risk their life to get here.
“MPs must vote against this awful Bill, and stand up for refugees and the right to ask for protection.
"Instead of introducing yet more punitive laws, this Government should be focussing on urgently opening safe routes for refugees, like a refugee visa.”
People smuggler gets 30 month sentence
14:43 , Rachael Burford
As the debate on the Rwanda Bill rages on, the Home Office has released shocking details of a people smuggler caught by Border Force.
Jozef Balog, a Slovakian national, was sentenced to two-and-a-half years for assisting unlawful immigration.
Startling photos, taken by immigration officers, show the woman victim wedged inside a tiny, custom-built hideaway behind a Vauxhall Vectra’s glovebox as she was smuggled into the country. Full details of the case can be read here.
Labour opposed to Rwanda scheme 'in its entirety'
14:24 , Rachael Burford
Labour opposes the "unaffordable, unworkable and unlawful" Rwanda Bill in "its entirety", says shadow immigration minister Stephen Kinnock
In order for the threat of deportation to Rwanda to be an "effective deterrent" it has to be "credible", he tells MPs.
But there is such a "tiny chance" of migrants being sent to the east African nation and it is never going to deter desperate people fleeing war and famine.
Dozens of judges brought in to speed up migrant appeals
14:06 , Rachael Burford
Freeing up courtrooms to speed up migrant appeals show the Government is "taking every conceivable step" to get deportation flights off the ground, Downing Street insisted.
It is understood 150 judges could be brought in to deal with cases, as part of efforts to quell concerns from rightwing Tory MPs threatening to rebel on the Rwanda Bill.
The Prime Minister's official spokesman said that while the Bill would ensure the bar for legal challenges is "set extremely high", it is "also right to ensure that we have the resources to deal with the minority of claims should they arise".
When it was put to him that some rebels argued the move was an acknowledgement that it would not put a stop to legal challenges, the Number 10 official replied: "No, I think it demonstrates that we are taking every conceivable step to ensure that we can get flights off the ground as quickly as possible.
"The spurious challenges we have seen before will be blocked through the Bill, the systemic challenges will be blocked.
"We have heard from leading judges, leading lawyers, who say the Bill will do the job that it needs to do, whether that is blocking challenges on modern slavery, on asylum - those sorts of spurious challenges will not be allowed.
"But it is right, in the small minority of cases, that we have resources put in place if needed."
Robert Jenrick: Current bill 'doesn't work'
13:52 , Rachael Burford
"The current bill doesn't work," Tory MP Robert Jenrick tells the Commons.
He quit as Immigration Minister over the plan, stressing it doesn't go far enough, and has helped draft a raft of amendments, including one that would block injunctions on flights taking off to Rwanda.
Illegal migration is leaving a "trail of human misery" Jenrick says.
13:42 , Rachael Burford
The SNP's Alison Thewliss kicks off the debate.
She brands it "awful" and says Rwanda is an "unsafe" country to deport people to.
"It is not compatible with international refugee law," she says.
13:33 , Rachael Burford
Ahead of Rishi Sunak's high-stakes Commons showdown with his own MPs, Boris Johnson stepped in to back the Tory right wing rebels seeking to change the Rwanda Bill. The former PM waded into the Conservative infighting by tweeting: “This bill must be as legally robust as possible - and the right course is to adopt the amendments."
Read all the background ahead of the debate here.