The prime minister is continuing to consider her next move to break the Brexit deadlock following the latest defeat of her withdrawal plan.
Senior government sources say the “ambition” is still to get Theresa May’s deal through the Commons.
But MPs will again vote on alternatives on Monday, with a customs union with the EU thought to be MPs’ most likely preferred option.
Some senior Brexiteers have warned Mrs May against pursuing such a move.
The prime minister has until 12 April to seek a longer extension to avoid the UK leaving without a deal.
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Mrs May said the UK would need “an alternative way forward” after her plan was defeated by 58 votes on Friday, following earlier defeats by 230 and 149 votes.
The government has so far failed to win over 34 Conservative rebels, including both Remainers and Brexiteers, who say Mrs May’s deal still leaves the UK too closely aligned to Europe.
Northern Ireland’s DUP – which has propped up the minority Tory government – also continues to oppose the deal.
But a No 10 source indicated the prime minister would continue to seek support in the Commons and insisted efforts were “going in the right direction”.
BBC political correspondent Alex Forsyth described the cabinet as “deeply divided” over what steps to take next.
MPs from all parties will test support for some other options during a second round of indicative votes on Monday.
None of MPs’ eight proposed Brexit options secured a majority in the first set of “indicative votes” on 27 March, but those which received the most votes were a customs union with the EU and a referendum on any deal.
The customs union allows businesses to move goods around the EU without checks or charges. Continued membership would bar the UK from striking independent trade deals after Brexit.
However, Conservative Party chairman Brandon Lewis said the government did not support any of those options.
Mr Lewis told BBC Radio 4’s Today programme: “The government’s position is very clear – we do not support these options. The government’s position is we believe the best way to respect the referendum is to deliver the deal.”
He said staying in a customs union with the EU would go against the result of the referendum and the Conservatives’ election manifesto.
Labour leader Jeremy Corbyn said his party would propose a deal that did involve a customs union with the EU – to protect the issue of avoiding a hard border in Northern Ireland.
He said: “I’m convinced of that after spending a lot of time meeting with and talking to officials in Europe.”
Tory Brexiteer Andrew Bridgen said leaving the EU without a deal was the best option on the table.
“No deal is the only way we’re going to get out, fulfilling our manifesto pledges and the commitment we made to the British people after the referendum,” he said.
Fellow Tory MP and former cabinet minister Nicky Morgan said one way to end the Brexit deadlock could be a government of national unity – a cabinet made up of different parties.
She told Today: “There have been periods in our history when we have had national unity governments or a coalition for a very specific issue.”
Commons leader Andrea Leadsom said she remained “confident” the government could deliver Brexit, adding that “we have to keep trying”.
Mrs May has said it is “almost certain” there would have to be an extended delay to Brexit to allow the UK to take part in the European elections at the end of May if her deal does not go through.
But Downing Street later said this was not an “inevitability”.
The withdrawal agreement is the part of the Brexit deal Mrs May struck with Brussels which sets out how much money the UK must pay to the EU as a settlement, details of the transition period, and the Irish backstop arrangements.
If Mrs May wants to hold another vote on the deal in Parliament, it has to comply with Commons Speaker John Bercow’s ruling that it can only be brought back with “substantial” changes.
This is why the government separated the withdrawal agreement from the political declaration – on the future relationship with the EU – for Friday’s vote.
What happens next?
- Monday, 1 April: MPs hold another set of votes on various Brexit options to see if they can agree on a way forward
- Wednesday, 3 April: Potentially another round of so-called “indicative votes”
- Wednesday, 10 April: Emergency summit of EU leaders to consider any UK request for further extension
- Friday, 12 April: Brexit day, if UK does not seek/EU does not grant further delay
- 23-26 May: European Parliamentary elections
Following Friday’s vote, Mrs May said there would be “grave” implications and warned they were “reaching the limits of this process in this House”.
Her comments led some to speculate the PM could try to call a general election.
However, Foreign Office minister Sir Alan Duncan told The Observer: “If we have a general election before Brexit is resolved, it will only make things worse.”
Under the terms of the Fixed Term Parliaments Act, the prime minister needs a two-thirds majority in order to call an election.
Brexit: Theresa May considers next step to break deadlock}