MPs have backed seeking “alternative arrangements” to replace the Irish backstop in Theresa May’s Brexit plan.
The proposal – put forward by Tory MP Sir Graham Brady – had the support of the government and won by 16 votes.
Theresa May had urged MPs to vote in favour of it, to give her a mandate to return to Brussels and re-open negotiations in order to secure a “legally binding change”.
But the EU has said it will not change the legal text agreed with the UK PM.
MPs voted on a string of amendments to Mrs May’s plan to change the direction of Brexit.
Mrs May said that, after taking the votes into account and talking to the EU, her revised deal would be brought back to the Commons “as soon as possible” for a second “meaningful vote”.
Another amendment, rejecting a no-deal Brexit, also won the support of Parliament on Tuesday, but the vote was not binding – meaning the date for exit remains 29 March.
Labour leader Jeremy Corbyn said as a result of the message from MPs rejecting no deal, he would now meet the prime minister to discuss the next steps.
He had previously refused to meet her unless she ruled out a no deal Brexit herself.
Five other amendments, including Labour MP Yvette Cooper’s bid to delay Brexit if Mrs May does not get her deal through Parliament, were defeated.
The controversial backstop element of Mrs May’s original plan is the insurance policy to prevent checks on goods and people returning to the Northern Ireland border, which some MPs fear could leave the UK tied to the EU’s rules indefinitely.
It was one of the main reasons her Brexit deal was voted down in Parliament by an historic margin earlier in January.
Mrs May hopes the support for Sir Graham’s amendment – which won by 317 votes to 301 – to look at alternatives gives her a stronger negotiating position with the EU.
She told the Commons there was now a “substantial and sustainable” majority of MPs supporting leaving the EU with a deal, but admitted renegotiation “will not be easy”.
Mr Corbyn said: “Parliament has voted to remove the immediate threat of crashing out without a deal on 29 March.
“After months of refusing to take the chaos of no deal off the table, the prime minister must now face the reality that no deal is not an option.”
The leader of the Democratic Unionist Party in Westminster, Nigel Dodds, said it was a “significant night” and his MPs would work with the prime minister “to deliver the right deal for the United Kingdom”.
But the leader of the SNP in Westminster, Ian Blackford, said that passing the amendment had seen the government “rip up the Good Friday Agreement” – integral to the peace process in Northern Ireland.
Liberal Democrat leader Sir Vince Cable said the Commons had given the prime minister “contradictory instructions to have no deal but pursue a course of action that will lead to a no deal”.
By BBC Political Correspondent Ben Wright
MPs had the chance to take more control over the Brexit process but didn’t.
After a torrid two weeks for the government, tonight brought some relief for its whips.
Tory MPs cheered as the Dominic Grieve amendment was kicked out by a comfortable margin.
It would have ensured six days of Parliamentary time for MPs to test the support of various Brexit scenarios.
The government benches delighted in the defeat of Yvette Cooper’s amendment too, which could have ensured a “no deal” Brexit was blocked.
However, in narrowly passing the Caroline Spelman/Jack Dromey amendment, MPs have said they do not want a “no deal” Brexit.
The government is not compelled to comply, but the political point has been made.
Theresa May has set herself a very high bar in the days ahead: to secure legally binding changes to a withdrawal deal EU leaders insist is closed.
The prime minister’s decision to return to the negotiation table was enough to swing her own Brexiteers behind the Downing Street-endorsed amendment by Sir Graham Brady.
It called for “alternative arrangements” to the Irish backstop, but it’s not clear what those alternative arrangements might be.
The drama will now move quickly to Brussels and the government’s respite might be brief.
Speaking after the result, President of the European Council Donald Tusk said the withdrawal deal is “not open for re-negotiation” and “remains the best and only way to ensure an orderly withdrawal of the United Kingdom from the European Union”.
He said the EU would be willing to look at the political declaration again – the part of the deal that makes a pledge on the future relationship between the UK and the EU – and that the EU would “stand ready” to consider any “reasoned request” for an extension to the leave date of 29 March.
But he concluded: “We will continue our preparations for all outcomes, including a no-deal scenario.”
A statement from the Irish government said the withdrawal agreement is “a carefully negotiated compromise, which balances the UK position on customs and the single market with avoiding a hard border and protecting the integrity of the EU customs union and single market.”
What happens next?
The prime minister has invited Tory MP Caroline Spelman, Labour MP Jack Dromey and others who tabled amendments to prevent a no deal to discuss how to move forward and secure a deal for Brexit.
She also invited Mr Corbyn for talks and promised the government would “redouble its efforts to get a deal this House can support”.
Mrs May has said she will speak to Brussels about changing the deal.
Her revised deal will return to the Commons to be voted on. But, if it is again rejected, the government will table an amendable motion for debate the following day.
And if no new deal is agreed by Parliament by 13 February, she will make a statement and, again, table an amendable motion for debate the next day.