The cabinet minister, who had previously been a staunch supporter of Boris JohnsonPeston told ITV he had handled things “horribly” in recent days.
She said: “The balance has now tipped in favor of saying the Prime Minister – it pains me to say it – but it is time to go.”
She said she will put her name in the ring if there is a leadership contest.
She told Peston: ‘My first duty is to the country, Robert, and as a lawyer I am the senior law officer.
“And we’re in a crisis and I have statutory legal and constitutional duties…
“I don’t want to resign because I have that duty. We need a lawyer in the government.”
When asked whether she acknowledges that Mr Johnson is likely to fire her, she said: “That is his choice, and I will do what the Prime Minister asks.”
The prime minister on Wednesday rejected calls to quit and dramatically fired the cabinet rival Michael Govebut was later affected by the departure of a third minister – Welsh Secretary Simon Hart – and the demand from Mrs Braverman.
The withdrawal of the Attorney General’s support marks a major shift by the QC, who was elected MP for Fareham in May 2015 before being appointed by Mr Johnson as the top legal officer in February 2020.
She became the first cabinet minister to take maternity leave and was reappointed to her ministerial position in September.
Special legislation had to be passed by Parliament to allow her to take time off from her ministerial duties.
During her absence, she was designated as a minister on leave (Attorney General), while her deputy, Solicitor General Michael Ellis, became Attorney General.
During last month’s confidence vote, Ms Braverman expressed hope that the Prime Minister would win the poll by a wide margin.
The Eurosceptic has been a supporter of Johnson since her days as chair of the Brexit-supporting European Research Group.
But Mrs Braverman joined Home Secretary Priti Patel on Wednesday, Home Secretary Kwasi Kwarteng, Transport Secretary Grant Shapps, Northern Ireland Secretary Brandon Lewis and Minister for Wales, Simon Hart, among the cabinet ministers who say Johnson is stepping down.