MPs are debating four amendments ahead of another crunch Brexit vote on whether to request an extension of Article 50.
Commons Speaker John Bercow has selected four main amendments for the debate on extending the Brexit process:
Amendment H, tabled by Independent Group MP Sarah Wollaston and which seeks an Article 50 extension to stage a second referendum with Remain and Parliament's preferred Brexit option on the ballot paper.
Amendment I, tabled by Labour's Hilary Benn and which seeks to allow MPs to take control of the Brexit process.
Amendment E, Labour's amendment which notes that Parliament has "decisively" rejected both Theresa May's deal and no deal and calls for a delay to Brexit "to provide parliamentary time for this House to find a majority for a different approach".
Amendment J, Labour MP Chris Bryant's amendment to stop a third meaningful vote on Mrs May's deal.
They do not include amendment B, which sought to reject a second Brexit referendum.
ITV News Political Correspondent Paul Brand confirmed the order of tonight's votes, with Amendment H scheduled to be first, although this could be pulled.
The action in the House of Commons comes a day after a cabinet rebellion helped to rule out the possibility of a no-deal Brexit entirely.
Chancellor Philip Hammond confirmed he will vote for the Article 50 extension as he urged the divided House of Commons to "work relentlessly" towards a compromise and back the PM's twice-defeated deal.
Mr Hammond admitted he had been "of course tempted" to abstain with his some of cabinet colleagues in Wednesday night’s no-deal vote but said "different people came to different conclusions".
Parliamentarians voted 321 to 278 on Wednesday, a majority of 43, to rule out the prospect of leaving the EU without a deal at any time.
Theresa May insisted however that no-deal remains her default option if an agreement can not be struck.
It came 24 hours after Mrs May's Withdrawal Agreement was rejected comprehensively for a second time.
Video report by ITV News Political Correspondent Romilly Weeks
The prime minister confirmed that MPs will vote on Thursday whether to seek an extension of Article 50 until June 30.
Any extension beyond that date would likely require the UK to participate in the European Parliament elections, the government warned.
Donald Trump has said the ongoing debate in Britain over leaving the European Union is "tearing the country apart."
He said both sides are very "cemented in" and he called Brexit negotiations a "tough situation" and a "shame."
On Thursday, the US president said he is "surprised at how badly" it has been handled and he thinks an agreement to leave the EU could have been negotiated better.
He said he gave advice to Mrs May but added that she didn't listen to him.
Trump commented as he welcomed Irish Prime Minister Leo Varadkar to the White House for an early St. Patrick's Day celebration.
Meanwhile ITV News Political Editor Robert Peston said the latest vote represented a "huge setback" for Mrs May.
The prime minister said "the options before us are the same as they always have been".
"The House has today provided a clear majority against leaving without a a deal, however I will repeat what I said before," she said.
"These are about the choices this House faces. The legal default in EU and UK law is that the UK will leave without a deal unless something else is agreed. The onus is now on every one of us in this House to find out what that is.
"The options before us are the same as they always have been."
Labour leader Jeremy Corbyn said that Parliament must now take control of the Brexit process and his party will work across the House of Commons to seek a compromise solution.
Within moments of the result, Sarah Newton resigned as a minister at the Department for Work and Pensions - citing the Brexit vote.
A motion whether to rule out no-deal solely on 29 March was initially intended to be voted on, but a successful amendment changed this to all dates and times.
Dame Caroline Spelman had attempted to withdraw her amendment but it was moved by fellow signatory Yvette Cooper during a string of crunch Brexit votes on Wednesday evening.
MPs voted 312 to 308 in favour of the amendment.
In a further amendment, MPs rejected the option to seek an Article 50 extension until May 22 by 374 votes to 164.
Speaking of delaying Brexit, Mrs May said: "If the House finds a way in the coming days to support a deal it would allow the government to seek a short limited technical extension to Article 50 to provide time to pass the necessary legislation and ratify the agreement we have reached with the EU.
"But let me be clear such a short technical extension is only likely to be on offer if we have a deal in place.
Therefore the House has to understand and accept that if it is not willing to support a deal in the coming days and is it not willing to support leaving without a deal on 29th March, then it is suggesting that there will need to be a much longer extension to Article 50.
"Such an extension would undoubtedly require the UK to hold European Parliament elections in May 2019. I do not think that would be the right outcome. But the House needs to face up to the consequences of the decisions it has taken."
The prime minister's spokesman said there were no plans to go back to Brussels for more negotiations.
And asked whether a deal needed to be passed before the European summit, he said: "If the House wishes for the prime minister to be in a position where she can request only a short technical extension then a deal would have to be agreed before the end of next week."
Which Tory ministers abstained from the vote?
Business secretary Greg Clark
Defence minister Tobias Ellwood
Justice secretary David Gauke
Business minister Richard Harrington
Culture minister Margot James
Work and Pensions secretary Amber Rudd
Scotland secretary David Mundell
In all, nine Tory MPs voted against the government, including Ken Clarke, Justine Greening, Dominic Grieve and Sam Gyimah.
Scotland secretary David Mundell, who abstained, said that he had "always opposed" a no-deal Brexit.
He tweeted: "The PM has my full support in her objective of leaving the EU with a deal to deliver an orderly Brexit."
A Downing Street source said that ministers who voted against the government would be expected to resign.
But they added that ministers who abstained would not be expected to quit.
Peston said it was "literally extraordinary" these ministers would be allowed to continue, arguing that Mrs May had "surely lost all authority".
Tory MP Simon Clarke said he felt like he now had a "gun to his head"
"I think voters will appreciate we're increasingly getting a very, very limited range of options left if we want to actually honour the manifesto commitment to leave at all," he said.
"So it's now effectively a bad Brexit deal or no Brexit. It's absolutely ghastly."
ITV News Europe Editor James Mates explains Strasbourg's reaction to Westminster's rejection of a no-deal Brexit