Chancellor Philip Hammond said talk of a change was "self indulgent" while Brexit Secretary Stephen Barclay said the PM "is in charge".
David Lidington - one of those touted as a possible replacement - insisted: "I am 100% behind the prime minister."
Mr Barclay told the BBC a general election would 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 the Brexit secretary said they would "not be binding".
'Serious manoeuvring
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, Mrs May's de factor deputy who voted Remain, is being lined up, while the Mail on Sunday said the Brexiteer Environment Secretary Michael Gove was the "consensus choice".
The BBC's political editor, Laura Kuenssberg says there is "serious manoeuvring" going on.
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
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".
Mr Lidington insisted Mrs May was "doing a fantastic job" and he had not desire to take over from her.
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.
'Crisis'
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".
David Lidington - one of those touted as a possible replacement - insisted: "I am 100% behind the prime minister."
Mr Barclay told the BBC a general election would 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 the Brexit secretary said they would "not be binding".
'Serious manoeuvring
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, Mrs May's de factor deputy who voted Remain, is being lined up, while the Mail on Sunday said the Brexiteer Environment Secretary Michael Gove was the "consensus choice".
The BBC's political editor, Laura Kuenssberg says there is "serious manoeuvring" going on.
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
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".
Mr Lidington insisted Mrs May was "doing a fantastic job" and he had not desire to take over from her.
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.
'Crisis'
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".
