The former Brexit secretary called on Conservatives not to “resign themselves to the coming electoral car crash”, and if they do not believe in the PM to “be doing something about it”.
As Mr Sunak faces mounting pressure over his beleaguered Rwanda deportation plan, Lord Frost said: “If there is anything to be done to get us on a better path and increase our chances of winning, then I believe it must be done.”
The intervention comes ahead of a showdown vote for Mr Sunak in parliament on Tuesday.
He is facing opposition from both the Tory left and right-wing MPs over plans to rule Rwanda a “safe” country by law to allow Britain to deport asylum seekers there.
MPs on the right of the Conservative Party believe the measures set out by Mr Sunak are not tough enough to ensure flights take off.
Meanwhile some centrist Tories believe the bill, which would disapply the Human Rights Act in a bid to prevent asylum seekers lodging appeals, is too extreme.
The opposition could lead to a major Commons defeat for Mr Sunak, which would raise questions about his ability to continue as PM.
It is only the latest headache for Mr Sunak, whose popularity among Conservative Party members plunged to a record low this week - more than a year after taking over as PM.
He is consistently around 20 points behind Sir Keir Starmer in the polls and has faced major unrest on the back benches.
And, in a significant intervention on Friday, Lord Frost said the Conservatives seem “resigned to the coming electoral car crash” with Mr Sunak as leader.
In an article for the Daily Telegraph, he warned that by resigning themselves to defeat the Conservatives were paving the way for a Labour government to bring Britain closer in line with the EU.
Lord Frost said: “I don’t want to lose, I don’t believe we have to lose, and I am not prepared to give up without a fight. It’s obvious the current strategy is not working. The Conservative Party is frozen rigid in its enemies’ gaze.
And, in an attack on Mr Sunak, he said: “The polls are getting worse, not better. If we are to get back those 2019 voters then we won’t do it by tilting further back to Camero-Blairism, by smoking bans or tinkering with A-levels, or by failing to deliver on crucial commitments like immigration.”
Lord Frost called for the party to set out a “mainstream Conservative path” on issues such as taxation, spending, the culture wars, net zero, migration and public service reform.
And in a plea to Tory MPs, he said: “If there is anything to be done to get us on a better path and increase our chances of winning, then I believe it must be done.” He called for the Rwanda bill to be improved so that it “does the job”.
“But MPs also have a responsibility to consider more broadly whether they think the current path can take us to an election win. If they don’t, they shouldn’t be resigning themselves to it – they should be doing something about it,” Lord Frost added.
Tory chairman Richard Holden said on Thursday that replacing the PM and ushering in yet another Tory leadership contest was “insanity”.
Meanwhile Tory veteran Sir Charles Walker – former 1922 committee chairman – said an election would have to be called if a “ridiculous” vote in Mr Sunak’s leadership was triggered. “If the threshold of 50 or so letters was crossed then the idea of another leadership [vote] is a nonsense – we have to go straight to a general election,” he told the News Agents podcast.