Braverman, the home secretary responsible for policing and national security, has a long history of making controversial statements that have alienated her more moderate colleagues.
In an opinion piece in The Times published ahead of a pro-Palestinian march on Saturday, Braverman accused the police of exhibiting a "double standard" in the way they treat protests, notably pro-Palestinian demonstrations.
Braverman, seen as a possible candidate to be the next leader of the governing Conservative Party, has repeatedly criticised the tens of thousands of protesters who have gathered in London since the Hamas attack on Israel last month.
The home secretary has called the protests "hate marches" and "mobs", despite the fact they have not led to overt violence.
Some Conservative Party politicians called for her to be moved or distanced themselves from her comments on Friday.
Geoffrey Clifton-Brown, treasurer of the Conservative's influential 1922 Committee that governs its backbench lawmakers, said Braverman's comments were "unwise" and "unprecedented", and that Sunak must consider moving her to a different role.
"We cannot carry on as we are. This is completely unacceptable, to carry on as we are on these very, very sensitive matters," he told the BBC.
Sunak, whose party is heavily trailing the main opposition Labour Party in the opinion polls, must decide whether to sack the most disruptive member of his cabinet, who could be a rival and critic if she was removed.
While ministers have repeatedly called for Saturday's rally - which coincides with the anniversary of Armistice Day, the end of World War One - to be cancelled, London's police have said the threat of violence was not high enough for them to use legal powers to ban it.
Downing Street is conducting an investigation into how the Times article was published on Wednesday after officials in Sunak's office demanded changes to its content that did not appear.
Under the government's code of conduct, ministers must seek approval from Downing Street for all major announcements, speeches, press releases and new policy initiatives. Since the article was published, Braverman has not apologised.
Opposition leader Keir Starmer has said Sunak is too weak to fire her.
Britain's finance minister, Jeremy Hunt, was the most senior member of the government to distance himself from Braverman's comments on Friday.
"The words that she used are not words that I myself would have used," he said.
(Reporting by Andrew MacAskill; Editing by Jan Harvey)
By Andrew MacAskill
