Mrs May declined to put a date on her departure, and said she would not stand down as soon as the UK leaves the EU, but will not lead the party into the election scheduled for 2022.
Mrs May won Wednesday’s confidence vote by 200 votes to 117, a margin that has failed to quell divisions over Brexit or demands for her to quit.
And Dominic Raab, the former Brexit Secretary, said on Thursday morning that “it looks very difficult to see how this Prime Minister can lead us forward”.
Loyalists hit back, with one minister comparing members of the pro-Brexit European Research Group to ants surviving a nuclear holocaust.
"They never, ever stop,” said Foreign minister Alistair Burt. “Votes against them, letters going in late - nothing matters to ERG.
"After the apocalypse, all that will be left will be ants and Tory MPs complaining about Europe and their leader."
Arriving at the European Council summit in Brussels, Mrs May was asked to confirm publicly the promise she made behind closed doors to Tory MPs as she sought their support on Wednesday.
"But I think it is right that the party feels that it would prefer to go into that election with a new leader."
Asked whether she has a date in mind, she said: "No. People try to talk about dates. What I'm clear about is the next general election is in 2022 and I think it's right that another party leader takes us into that general election."