The Mayor of London said violent clashes involving counter-protesters were a "direct result" of the HomeSecretary's words, after she accused the Metropolitan Police of bias towards "pro-Palestinian mobs".
The capital experienced major unrest on Armistice Day, with more than 100 people detained as far-Right groups clashed with police.
It came as 300,000 demonstrators descended on London for a huge march protesting Israel's strikes on Gaza.
Mr Khan said it was “disturbing” to see violence towards police and urged the Prime Minister to sack Ms Braverman.
“Sadly, these scenes were predictable after a week of efforts from some to stoke tension,” Mr Khan wrotein the Sunday Mirror.
“They were a direct result of the Home Secretary’s words and behaviour.”
“If Suella Braverman had any honour she would resign – and if not, Rishi Sunak should sack her.”
Nine officers were injured as they prevented a crowd reaching the Cenotaph. Met Police Assistant Commissioner Matt Twist called the “extreme violence” towards officers “extraordinary and deeply concerning”.
“A week of intense debate about protest and policing” helped “increase community tensions”, he said.
Mr Sunak has so far maintained confidence in Ms Braverman despite many within her own party distancing themselves from her remarks.
In a comment piece in the Sunday Telegraph, Labour leader Sir Keir Starmer wrote: “The Home Secretary and the Prime Minister’s treatment of the police and protestors alike this week – coming just a few days after she shamefully described homelessness as ‘a lifestyle choice’ – betray a total lack of respect for this country’s values and its principles.
“Few people in public life have done more recently to whip up division, set the British people against one another and sow the seeds of hatred and distrust than Suella Braverman. In doing so, she demeans her office.”
Sir Keir said some among the pro-Palestinian demonstrators incited violence, glorified Hamas or called for Israel’s destruction and “should be dealt with firmly by the law”.
But he said blanket calls to cancel the rallies and Government attempts to brand protesters they do not agree with as extremists are “a sign of ministers’ cowardice”.
Shadow home secretary Yvette Cooper said: “Suella Braverman was warned repeatedly of the dangers of inflaming tensions and undermining the police.
“A Home Secretary that doesn’t take seriously the security of our streets is only allowed to remain in a government that has lost all sense of governing. Britain is better than Rishi Sunak and his Cabinet.”
Scottish First Minister Humza Yousaf earlier called for Mrs Braverman to resign.
The SNP leader tweeted: “The far right has been emboldened by the Home Secretary. Shehas spent her week fanning the flames of division. They are now attacking the police on Armistice Day.
“The Home Secretary’s position is untenable. She must resign.”
Hope Not Hate echoed the demand, with the campaign group’s chief executive Nick Lowles saying the Home Secretary has “inflamed tensions and, as we have seen today, whipped up the far right into a violent frenzy. She’s got to go”.
But Ms Braverman has supporters on the right of the party and her removal could deepen divisions within Tory ranks.
Conservative former minister Brendan Clarke-Smith defended the Home Secretary, saying: “I’ve heard some daft takes, but to try and justify this appalling behaviour by blaming an op-ed in The Times, which simply stated the flaming obvious, is pathetic.”
Tory backbencher Danny Kruger said: “You know what, with the benefit of hindsight, maybe it would have been best if the march today hadn’t been allowed to go ahead.”
Ms Braverman rowed back her language on the eve of Armistice Day, giving police her “full backing”at a meeting with Metropolitan Police Commissioner Sir Mark Rowley.
It came after her article in The Times, in which she claimed officers “play favourites”towards pro-Palestinian protesters, was disowned by Downing Street and provokedfury among Tory MPs.