British Prime Minister Theresa May vowed to fight off any challenge to her leadership hours before she met her reshuffled cabinet for the first time on Tuesday.
Foreign secretary Boris Johnson and Brexit secretary David Davis both quit within 24 hours of each other over her plans for departing the European Union, which was agreed on Friday.
The prime minister tweeted a picture of the meeting, describing the discussion as "productive".
The resignation of the two senior ministers as well as three junior ministers has fuelled speculation that Mrs May will face a vote of no confidence in the coming days.
The vote could be triggered if 48 politicians from her party write to the chairman of the 1992 Committee (the parliamentary group of the Conservative party).
On Monday night, a Downing Street source confirmed that Mrs May would fight challenges to her leadership.
The prime minister warned members of her party that continuing to fight over her Brexit proposals would hand her opposition rival, Labour leader Jeremy Corbyn, an easy victory.
Mrs May’s authority was greatly weakened last year after she called an ill-judged snap election and the Conservatives lost their parliamentary majority. The vote was seen as an unexpected success for socialist Mr Corbyn, who, despite coming behind the Conservatives, oversaw a swing back to Labour. In order to form a government, Mrs May had to make an alliance with the Democratic Unionist Party, a small right-wing party from Northern Ireland.
Supporters rallied round the prime minister, including newly appointed Foreign Secretary Jeremy Hunt, who said he would be “four-square” behind her.
Speaking on Tuesday, Justice Secretary David Gauke rebuffed criticism of the UK’s proposals for a trade relationship with the EU after it leaves the bloc on March 29, 2019.
“If people don't like this [Brexit] proposal, what's their alternative?” he told BBC radio.
However, the most recent upheaval in government caused by the resignations has heightened fears that the UK will leave the bloc without a deal in place, something Mr Gauke said the government was preparing for.
“It's not an attractive proposition for the UK or EU, which is why we should move these negotiations to the next stage," he said.
Mrs May has proposed to keep close economic ties with the EU, the world’s largest trading bloc, seen to be an acceptance of a so-called “soft Brexit” desired by British business leaders. Negotiations with Brussels are set to continue over the summer ahead of an EU summit in October.
In Mr Johnson’s resignation letter to the prime minister, he said that the strategy showed that the UK was “truly headed for the status of colony” and accused her of pursuing a “semi Brexit”.
In her reply, Mrs May said she was “sorry, and a little surprised”.
But she said: “If you are not able to provide the support we need to secure this deal, in the interests of the United Kingdom, it is right that you should step down.”
Speculation over whether the departure of the two leading Brexiteers might lead to a reversal of the EU referendum vote began on Monday after EU council President Donald Tusk implied the whole thing might be called off.
“Politicians come and go but the problems they have created for people remain,” Mr Tusk wrote in a suggestive tweet that was later pinned to the top of his social media profile. “I can only regret that the idea of #Brexit has not left with Davis and Johnson. But ... who knows?”