It is now “physically impossible” for the UK to leave the European Union on 29 March, the chancellor says.
Philip Hammond told the BBC’s Andrew Marr that even if MPs agreed the PM’s Brexit deal in the coming days, a “short extension” would be needed to pass the necessary legislation.
He said the deal might not go forward for a third Commons vote without more support from the DUP and other MPs.
Theresa May has asked MPs to make an “honourable compromise” on her deal.
Writing in the Sunday Telegraph, she said failure to support it would mean “we will not leave the EU for many months, if ever”.
Meanwhile, Labour leader Jeremy Corbyn has written to MPs across the Commons inviting them for talks to find a cross-party compromise.
He also told Sky’s Sophie Ridge that while he “has to see the wording of it”, Labour MPs would be told to vote in favour of an amendment calling for another referendum next week.
And he said he could propose another vote of no confidence in the government if the PM’s deal was voted down for a third time.
Earlier this week MPs rejected Theresa May’s deal again – this time by 149 votes – and then backed plans to rule out leaving the EU without a deal.
They also voted in favour of an extension to the process – either until 30 June if Mrs May’s deal is supported before 20 March, or a longer one that could include taking part in European elections if MPs reject her plan for a third time.
But legally the UK is still due to leave the EU on 29 March.
All 27 EU member states would have to agree to an extension, and the country’s leaders are expected to discuss it at a summit later this week.
Mr Hammond told Andrew Marr: “If the prime minister’s deal is able to muster a majority this week and get through, then we will need a short extension.
“It is physically impossible to leave on 29 March, but we would be able to leave very soon.
“But if we are unable to do that – if we are unable to bring a majority together to support what in my view is a very good deal for Britain – then we will have to look at a longer extension and we are in unchartered territory.”
Asked if the third so-called “meaningful vote” on the deal would definitely be returning to the Commons this week to seek such support, the chancellor said: “The answer to that is no – not definitely.
“We will only bring the deal back if we are confident that enough of our colleagues and the DUP are prepared to support it so we can get it through Parliament.
“We are not just going to keep presenting it if we haven’t moved the dial.”
‘Work in progress’
Mr Hammond said they did not have the numbers “yet” but added: “It is a work in progress. Obviously we are talking to a lot of colleagues about what the way forward is.
“But clearly if we don’t get this deal through, we are almost certainly going to have to fight a European parliamentary election [and] we are almost certainly going to have to have a longer extension.”
Mr Hammond also refused to rule out a financial settlement for Northern Ireland if the DUP backed Mrs May’s deal.
The party, which has 10 MPs in the Commons, received £1bn as part of a confidence and supply agreement with the Tories after the last election – giving the government a working majority.
The DUP’s Westminster leader, Nigel Dodds, met with senior cabinet members on Friday – including Mr Hammond – to discuss what it would take to get them onboard with the PM’s plan, but they said afterwards there were “still issues to be addressed”.
A group of 15 Tory MPs from Leave-backing constituencies, including former Brexit Secretary David Davis, have also urged colleagues to back the deal.
In a letter, the group claimed there were people “who will stop at nothing to prevent Britain leaving the EU”, adding they would vote for the deal to ensure Brexit went ahead.
“We urge colleagues who, like us, wish to deliver Brexit, to vote for the deal and ensure we leave the EU as soon as possible,” they said.
“We need to leave now, take the risk of ‘no Brexit’ off the table, and then continue to fight for the best future relationship as an independent nation.”
Former Cabinet minister Esther McVey, who resigned over the Brexit agreement, told Sky’s Sophie Ridge programme that she would “hold my nose” and vote for the deal after rejecting it twice herself, as it was now a choice between “this deal or no Brexit”.
But she later called on Mrs May to make a “dignified departure” from the top job.
Speaking to BBC Radio 5 Live’s Pienaar’s Politics, Ms McVey said the next Tory leader “would have to be a Brexiteer and the cabinet would have to be ‘Brexiteer-minded'”.
And she said that, if enough people asked her to stand, she would put herself forward in the next leadership contest.
Mr Corbyn has offered talks with opposition leaders and backbench MPs in an effort to find a Brexit compromise which could replace Mrs May’s plan.
The Labour leader has invited Liberal Democrat leader Sir Vince Cable, DUP deputy leader Nigel Dodds, SNP Westminster leader Ian Blackford, Plaid’s Liz Saville Roberts and Green MP Caroline Lucas.
In his letter, he called for urgent meetings to find a “solution that ends the needless uncertainty and worry” caused by Mrs May’s “failed” Brexit negotiations.
Meanwhile, Tory MP Nick Boles has pledged to stay in the Conservative Party, despite quitting his local association over an ongoing row about Brexit.
He told the BBC’s Andrew Marr that he would be meeting with the chief whip on Monday to find a way forward, but that he was “not going to be bossed around” by local members.
Mr Boles, who campaigned to stop a no-deal Brexit, said: “I will be my own kind of Conservative. Not an ideological reactionary Conservative.”