The British Prime Minister has said that MPs will vote tomorrow on an extension to Article 50.
Theresa May said that the move could involve a short delay to implement a deal agreed in the next few days, or a longer delay if no agreement is reached.
Mrs May's government has also set out plans for a third parliamentary vote on her Brexit deal with the EU to be held by 20 March.
In a proposal to be voted on by MPs tomorrow, the government states that if parliament has not approved the deal by that date it will ask the EU for an extension.
It comes after MPs voted in favour of an amended motion, which rejected the UK crashing out of the European Union without a deal at any time under any circumstances.
In a surprise move, the House of Commons voted 312 to 308 - a majority of four - in favour of the amendment tabled by Tory former cabinet minister Caroline Spelman.
Ms Spelman attempted to withdraw the amendment, but it was moved by fellow signatory Yvette Cooper and won the support of a majority of MPs during a string of crunch Brexit votes this evening.
The amendment is not legally binding, but it changes the British government's motion to say the House "rejects the United Kingdom leaving the European Union without a Withdrawal Agreement and a Framework for the Future Relationship".
However no-deal remains the default option unless an extension is agreed with the 27 other EU states, or a deal is passed before the end of the month.
To avoid a walkout by Cabinet ministers who oppose a no-deal Brexit, Mrs May has given Tories a free vote on the Government motion.
The wording of the motion declares the Commons "declines to approve" leaving without a deal on 29 March - but notes that remains the default position unless an agreement is reached.
Members of the Malthouse Compromise group of Tories from both Leave and Remain wings tabled an amendment calling for Brexit to be delayed until 22 May, followed by a "standstill" agreement lasting as late as the end of 2021, during which the UK would observe EU rules and pay into Brussels budgets while a full trade deal is negotiated.
This amendment was voted against, with 164 votes in favour of the amendment and 374 voting against.
The EU has already rejected the idea, which it views as amounting to a transition period without a formal Withdrawal Agreement.
The European Commission has said that it "takes note of the votes in the House of Commons this evening.
"There are only two ways to leave the EU: with or without a deal. The EU is prepared for both.
"To take no deal off the table, it is not enough to vote against no deal - you have to agree to a deal. We have agreed a deal with the Prime Minister and the EU is ready to sign it."
To sum up tonight: MP’s don’t want a no deal Brexit, underlines the deep divisions in govt, vote on extension tomorrow, Theresa May clearly believes her deal is not dead— Fiona Mitchell (@mitchefi) March 13, 2019
Sarah Newton, a minister at the Department of Work and Pensions, resigned after tonight's votes.
Commons votes 'not terribly surprising' - Foster
DUP Leader Arlene Foster has said that what happened tonight in the House of Commons is "not terribly surprising".
Speaking to RTÉ News in Washington, she said she knew there was always not a huge amount of support for a no-deal situation.
Ms Foster reiterated that nobody wants to see a no-deal Brexit scenario.
She said that the DUP is still working on a deal that does not leave Northern Ireland behind, and protects the "constitutional and economic integrity of the United Kingdom".
"I know people think that we are in the end game now but we should keep working right up until the very end to try and get a deal," she said.
Ms Foster did not rule out the US appointing a special envoy again to Northern Ireland, stating that what is important is the United States' willingness "to help is still existing".