Two ministers touted as a potential caretaker PM in reports of a cabinet coup say they fully back Theresa May.
Environment Secretary Michael Gove told reporters it was “not the time to change the captain of the ship”.
And the PM’s de facto deputy David Lidington insisted he was “100% behind” Mrs May.
Meanwhile, the Brexit secretary said an election will become more likely if MPs vote this week for a Brexit option the government does not want.
MPs are expected to get the chance to hold a series of so-called indicative votes on possible alternatives to Mrs May’s withdrawal deal, but Brexit Secretary Stephen Barclay said they would “not be binding”.
He was among the Tory MPs and ministers at talks with Mrs May on Sunday at Chequers, her country retreat.
Prominent Brexiteers Mr Gove, Boris Johnson and Jacob Rees-Mogg were also present.
They discussed a range of issues, including whether there was sufficient support to hold a third vote on the prime minister’s deal this week, a Downing Street spokesman said.
The prime minister has come under growing pressure to quit following a week in which she was forced to ask the EU for an extension to Article 50 and criticised for blaming the delay to Brexit on MPs.
The withdrawal deal she has negotiated with the EU has been overwhelmingly rejected in the Commons twice, and it remains unclear whether she will bring it back a third time next week after she wrote to MPs saying she would only do so if there was “sufficient support”.
They should be censured, sacked, or at the very least “they should be apologising and they should shut up,” he added.
MP for Aylesbury since 1992 and now Cabinet Office Minister, David Lidington, below left, is the prime minister’s right-hand man and behind-the-scenes fixer.
Mr Hammond said he would remove revoking Article 50 and a no-deal Brexit from the list, as “both of those would have very serious and negative consequences for our country”.
On the subject of a second referendum, he said: “It is a coherent proposition and deserves to be considered, along with the other proposals.”
But Mr Barclay said there was a “crisis” because “Parliament is trying to take over the government”.
He said if MPs vote for a Brexit outcome at odds with the Tory manifesto – for example, in favour of maintaining single market membership – “the risk of a general election increases, because you potentially have a situation where Parliament is instructing the executive to do something that is counter to what it was elected to do”.
Shadow Brexit secretary Keir Starmer said the indicative votes must be a “serious exercise”.He said Labour would go into the process “in good faith” but there needed to be “assurance that the prime minister isn’t going to use it just to frustrate the process”.
Labour chairman of the Brexit scrutiny committee Hilary Benn told Sky News MPs were just doing their job by attempting to take control of the process.
What’s happening this week?
Monday: MPs will debate the Brexit next steps and a number of amendments – possible alternatives – to the government plan will be put to a vote. One that could well succeed calls for a series of “indicative votes” in the Commons, run by Parliament, to see if a majority can be found for a different Brexit model.
Tuesday: Theresa May could bring her withdrawal deal back for the so-called third meaningful vote. But the government says it won’t do that unless it’s sure it has enough to support to win.
Wednesday: This is when indicative votes would be held – we don’t know yet whether MPs will be free to vote how they want or be directed along party lines. The chances of any genuine cross-party consensus being achieved are not high.
Thursday: A second possible opportunity for meaningful vote three. The prime minister may hope that Brexiteers will finally decide to throw their weight behind her deal because indicative votes have shown that otherwise the UK could be heading for the sort of softer Brexit they would hate.
Friday: This was the day the UK was meant to leave the EU. The earliest that will now happen is 12 April.
If Mrs May’s deal is approved by MPs next week, the EU has agreed to extend the Brexit deadline until 22 May.
If it is not – and no alternative plan is put forward – the UK is set to leave the EU on 12 April.