Theresa May will fight any attempt to unseat her through a vote of no confidence by Conservative MPs, Downing Street has said.
The defiant message came after Mrs May's administration was thrown into turmoil by the sensational resignations in quick succession of Brexit Secretary David Davis and Foreign Secretary Boris Johnson.
The departure of the two Cabinet "big beasts" came just two days after Mrs May secured senior ministers' agreement at Chequers for a Brexit plan about which both men had expressed reservations.
Mr Johnson's exit was announced by Downing Street moments before Mrs May faced the House of Commons to set out details of her plans.
The Prime Minister was greeted by loud cheers from Tory MPs and shouts of "resign" from the opposition benches as she arrived to deliver a statement in which she said her proposals would deliver "a Brexit that is in our national interest... the right Brexit deal for Britain".
The PM told MPs she wanted to recognise the work of the former Brexit secretary on steering through some of the "most important legislation for generations" and the "passion" that the outgoing foreign secretary had shown in promoting a "global Britain to the world".
But she said: "We do not agree about the best way of delivering our shared commitment to honour the result of the referendum."
Conservative MP Andrea Jenkyns said she believed that Mrs May's time as Prime Minister was "over", telling BBC Radio 4's Today programme that she wanted a premier who would "provide true leadership and a positive post-Brexit vision for our country".
And senior backbencher Bernard Jenkin said there had been a "massive haemorrhage of trust" in Mrs May.
Asked if Brexiteers needed to put the PM's future to a vote of the Conservative Party, he replied "it may well come to that".
However, prominent Brexiteer Jacob Rees-Mogg, the chairman of the European Research Group of Eurosceptic backbenchers, said he had not submitted a letter of no confidence and expected Mrs May to remain at least until the official date of Brexit in March 2019.
Some 48 Tory MPs - 15% of the party's 316-strong representation in the Commons - must write to the chairman of the backbench 1922 Committee, Sir Graham Brady, to trigger a no-confidence vote.
Sir Graham refused to say whether he had received any such letters.
And asked whether Mrs May would fight a no-confidence vote if one was called, a senior Number 10 source said simply: "Yes."
Mr Davis was first to go, announcing his exit just before midnight on Sunday.
But there was growing speculation about Mr Johnson's plans on Monday after he failed to attend a meeting of the Government's Cobra emergencies committee as well as a summit of Western Balkan nations being held in London.
At 3pm on Monday, a statement was issued by Downing Street to say: "This afternoon, the Prime Minister accepted the resignation of Boris Johnson as Foreign Secretary. His replacement will be announced shortly. The Prime Minister thanks Boris for his work."
Staunch Brexiteer Dominic Raab was named as Mr Davis's replacement as Secretary of State for Leaving the EU, and a new foreign secretary was expected to be in place by the end of the day.
There is added pressure for a swift appointment because the foreign secretary is due to join Mrs May at the Nato summit in Brussels on Wednesday and take part in the events of US President Donald Trump's visit to the UK, which begins on Thursday.
Mr Johnson was the figurehead of the Leave campaign in the 2016 referendum, but dramatically pulled away from an expected leadership bid after losing the support of fellow minister Michael Gove.
There was no immediate statement from Mr Johnson to explain his decision to quit, which was seized upon by opposition politicians as a sign of increasing turmoil within Mrs May's administration.