Theresa May must resign or the Conservatives should force her out, after the party’s heavy local election losses, Iain Duncan Smith has said.
The former Tory leader called Mrs May a “caretaker PM” and described her attempts to reach a Brexit deal with Labour as “absurd”.
The party suffered its worst local election result in England since 1995.
Other senior Conservatives have urged Tory MPs to compromise with Labour to ensure Brexit is delivered.
Elections were held on Thursday for 248 English councils, six mayors, and all 11 councils in Northern Ireland. No elections took place in Scotland or Wales.
The Conservatives lost 1,334 councillors, while Labour failed to make expected gains, instead losing 82 seats.
The Liberal Democrats benefited from Tory losses, gaining 703 seats, with the Greens and independents also making gains.
Following the results, Mrs May and Labour leader Jeremy Corbyn both insisted they would push ahead with talks seeking cross-party agreement on leaving the EU.
Mrs May said it was clear the public wanted “to see the issue of Brexit resolved”.
But Mr Duncan Smith, a leading Brexiteer, said many Conservatives would refuse to back any deal reached between the two parties.
Mrs May must announce her departure “very soon”, he said, and if she did not go, the 1922 Committee of backbench MPs would have to force her to do so.
Speaking to the BBC, he said: “As a result of the devastating election result, the PM has in effect become a caretaker.
“As such, she is not empowered to make any deal with the Labour Party which itself suffered a very similar result. Two discredited administrations making a discredited deal is not the answer to the electorate.”
In December, Mrs May survived a vote of no-confidence in her leadership of the Conservative Party, but in March she pledged to stand down if and when Parliament ratified her Brexit withdrawal agreement with the EU.
The UK had been due to leave the EU on 29 March, but the deadline was pushed back to 31 October after Parliament was unable to agree a way forward.
In the wake of the Conservatives’ local election losses, senior Tories have called for the party to compromise in order to reach an agreement with Labour to end the Brexit deadlock.
Scottish Tory leader Ruth Davidson called for the negotiating teams of both parties – who are currently locked in talks – to “get Brexit sorted, get a deal over the line and let Britain move on“.
Health Secretary Matt Hancock said the Conservative Party needed to listen to the election results and be “in the mood for compromise”.
Speaking to BBC Radio 4’s Today programme, he said the Conservatives might have to move towards Labour’s proposal of a permanent customs union – a move many Brexiteers in the party oppose – in order to solve the impasse in Westminster.
Mrs May’s government has previously ruled out remaining in a customs union after the UK leaves the EU, arguing it would prevent the UK from setting its own trade policy.
Labour has said the EU may show flexibility over the issue and allow the UK “a say” in future trade deals.
Mr Hancock suggested “coming up with something in-between”, and called for “an open dialogue in which we can make an agreement”.
But Mr Duncan Smith said a customs union was “the worst of all worlds because you lose your decision-making capacity”.
Meanwhile, Foreign Secretary Jeremy Hunt said there was a “glimmer of hope” that a compromise between the Conservative and Labour “core-voters” could be reached.
He added that while he supported the withdrawal deal reached between the EU and Mrs May, there might be things that could be done to make it “more acceptable” to Labour without compromising on the “things that we think are essential”.
But he also warned that a customs union would not be a “long-term solution”.
Shadow Brexit secretary Sir Keir Starmer said Mr Hunt’s remarks on a customs union provided “yet more evidence” that many in the cabinet believed the “most important thing right now” was the race to be Mrs May’s successor.
Labour’s MP for Redcar, Anna Turley, also reacted to Mr Hunt’s comments that a customs union was not a long-term solution, tweeting: “This is why we can’t trust the Tories by doing a deal stitched up in Number 10 which they will seek to unravel under their next leader.”