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.
Newspapers claim cabinet ministers are plotting a coup against the prime minister, aiming to replace her with a caretaker leader until a proper leadership contest is held later in the year.
The suggestion is that Tory MPs might reluctantly back Mrs May's Brexit deal if they know she will not be in charge of the next stage of negotiations with the EU, but there are differing accounts of who the preferred candidate to replace her is.
The Sunday Times reports that Mr Lidington, who voted Remain, is being lined up, while the Mail on Sunday said the Brexiteer Environment Secretary Mr Gove was the "consensus choice".
The BBC's political editor, Laura Kuenssberg says there is "serious manoeuvring" going on.
There is v serious manouvering going on this weekend which might change everything, or nothing https://t.co/eCuxCOhmnQ— Laura Kuenssberg (@bbclaurak) March 23, 2019
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".
One senior backbencher told the BBC's Iain Watson that even standing aside would not be enough for her deal to be voted through, and that Mrs May might as well "dig in".
Mr Gove said he was focused on getting the maximum amount of support for the prime minister and her Brexit deal.
And Mr Lidington insisted Mrs May was "doing a fantastic job" and he had no desire to take over from her.
Chancellor Philip Hammond told Sky's Sophy Ridge on Sunday "changing prime ministers wouldn't help, changing the party of government wouldn't help."
He denied reports he was hoping to parachute in Mr Lidington as caretaker, adding: "To be talking about changing the players on the board, frankly, is self-indulgent at this time."
Mr Hammond said he understood MPs were "very frustrated", but "one way or another Parliament is going to have an opportunity this week to decide what it's in favour of".
Former Conservative leader and prominent Brexiteer Iain Duncan Smith told the BBC's Andrew Marr the disloyalty some cabinet ministers were showing to her was "appalling".
They should be censured, sacked, or at the very least "they should be apologising and they should shut up," he added.
Lidington v Gove
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.
Once private secretary to William Hague when he was Tory leader, Mr Lidington was the longest-serving Minister for Europe under David Cameron and is clearly from the Remain camp. That makes him an unacceptable replacement for Theresa May in the eyes of Brexiteers.
Lidington is well-liked among fellow MPs and has an easy way with journalists, but he has attracted criticism from some quarters for his voting record, especially on LGBTQ rights. He voted against same sex marriage and to maintain a ban on the promotion of homosexuality in schools.
Former journalist turned MP for Surrey Heath, Michael Gove, above right, is currently environment secretary. He's previously held the justice and education briefs.
He and Boris Johnson helped lead Vote Leave to victory in the EU referendum, but Gove later ran against his former Brexit ally for the Tory leadership. He was subsequently sacked as a minister by Theresa May when she eventually won that contest.
Now having worked his way back into the senior echelons of government, Mr Gove is seen as someone who could hold the Conservative Party together, and might be a candidate Remainers could stomach because he's hinted he could be open to a softer form of Brexit. Arch Brexiteers feel, though, that for that very reason he'd be an unacceptable choice.
The leadership row comes ahead of a week where the PM is expected to lose further control over the Brexit process.
In the coming days, as many as six other options, in addition to Mrs May's deal, could be put to indicative votes in order to see which are most popular. They are:
- Revoking Article 50 and cancelling Brexit
- Another referendum
- The PM's deal plus a customs union
- The PM's deal plus both a customs union and single market access
- A Canada-style free trade agreement
- Leaving the EU without a deal
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 is written into law as the day the UK leaves the EU, although the PM has said she will pass legislation this week to remove it. The earliest Brexit is likely to happen is now 12 April.
Organisers said the initial count showed more than a million people had turned up - putting it on a par with the biggest march of the century, the Stop the War march in 2003.
Meanwhile, the woman behind a record-breaking anti-Brexit petition - which has received more than five million signatures - says she has received death threats over the poll.
Earlier in the week, European leaders agreed to delay the UK's departure from the EU.
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.