Mrs May has pledged to set a timetable for leaving Number 10 following another vote on her Brexit withdrawal agreement Theresa May’s successor as prime minister should not call a general election until Brexit is completed, a cabinet minister has warned.
Health Secretary Matt Hancock said an early election risked losing to Labour and "killing Brexit altogether".
His comments come after cross-party talks aimed at breaking the impasse collapsed on Friday.
Meanwhile, a poll of Tory members for The Times puts Boris Johnson as the favourite to succeed Mrs May.
Mr Hancock told the Daily Telegraph it would be a "disaster" to call a general election before the UK had left the EU as "people don’t want it".
He added: "We need to take responsibility for delivering on the referendum result." Why PM’s Brexit plan may not be dead yet
Brexit: What happens next?
A really simple guide to Brexit
"Who knows what the outcome of a general election would be under these circumstances? A general election before that not only risks Jeremy Corbyn, but it risks killing Brexit altogether."
Mrs May has promised to set a timetable for leaving Downing Street following a House of Commons vote on her EU Withdrawal Agreement Bill in the week beginning 3 June.
Brexit had been due to take place on 29 March – but after MPs voted down the deal Mrs May had negotiated with the bloc three times, the EU gave the UK an extension until 31 October.
This prompted talks between the government and Labour to see if they could agree a way to break the impasse but those negotiations ended this week without an agreement.
Mr Hancock said the current circumstances would make it difficult to predict the result of any general election before Brexit.
He added: "We’ve got to deliver Brexit in this parliament, then we can move forward." Your guide to Brexit jargon
Use the list below or select a button
– Choose a Brexit term –
A YouGov poll commissioned by The Times of Tory party members suggests that Boris Johnson is a favourite to succeed Theresa May as prime minister – he is the first choice to replace her for 39% of those polled.
Mr Johnson, who announced his intention to run earlier this week, was three times as popular as the next closest choice, ex-Brexit secretary Dominic Raab (13%).
Of the others, Home Secretary Sajid Javid and Environment Secretary Michael Gove were both on 9%, with Foreign Secretary Jeremy Hunt on 8% and Mr Hancock on 1%. Reality Check: How do you call an early election?
The hustings for next PM, in all but name
Johnson confirms bid for Tory leadership
Meanwhile, Labour leader Jeremy Corbyn is expected to declare that only Labour can halt the rise of the "far right" during a rally later.
Speaking ahead of the European parliamentary elections, he is expected to say that years of neglect had "opened the door" to the far right.
"Politics as usual won’t defeat them," he will say.
"We need Labour’s radical programme to transform our country and turn the tide of inequality by ending austerity and investing in our communities and people."