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".
It comes as Mrs May holds talks with colleagues and senior Brexiteers, including Boris Johnson, at Chequers, her country retreat.
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.