Theresa May has promised MPs a final, decisive vote on her Brexit deal with the EU - but not until she has secured changes to the Irish backstop clause.
The PM said she needed "some time" to get the changes she believes MPs want.
She promised to update MPs again on 26 February and, if she had not got a new deal by then, to give them a say on the next steps in non-binding votes.
Jeremy Corbyn accused her of "running down the clock" in an effort to "blackmail" MPs into backing her deal.
Britain is currently leaving the EU on 29 March, with or without a deal.
Labour claims Mrs May is planning to delay the final, binding vote on the withdrawal deal she has agreed with the EU until the last possible moment, so that MPs will be faced with a stark choice between her deal and no deal.
Labour and some Conservative MPs had been planning to have a fresh go at putting alternatives to Mrs May's deal to the vote on Thursday, in an effort to take control of the Brexit process.
But BBC Political Editor Laura Kuenssberg said Mrs May's announcement of returning to update MPs on 26 February and then more votes on 27 February - if she has still not got a final deal - meant Thursday's expected "high noon" for the prime minister had probably been postponed.
MPs are still expected to debate and vote on amendments to the Brexit deal on Thursday, however, although it will not be known until later what those amendments are likely to be.
May 'when we achieve the progress we need we will bring forward another meaningful vote' - but whatever happens, confirm vote on 27th -kills off most of the likely rebellious moves this week as expected, gives the Cooper-Boles gang another date in the diary - high noon postponed— Laura Kuenssberg (@bbclaurak) February 12, 2019
Mrs May promised to give MPs a "stronger and clearer role" in the next steps on Brexit and said she would return to the Commons for a meaningful vote on her deal "when we achieve the progress we need".
The PM said she was discussing a number of options with the EU to secure legally-binding changes to the backstop: Replacing it with "alternative arrangements", putting a time limit on how long it can stay in place or a unilateral exit clause so the UK can leave it at a time of its choosing.
The backstop arrangement is the "insurance" policy in Mrs May's deal to avoid a return to border checks on the island of Ireland.
The EU has reiterated it will not renegotiate the withdrawal agreement.
Mrs May said talks were at a "crucial stage", but she still believed it was possible to get a deal MPs could support.
"We now all need to hold our nerve to get the changes this House requires and deliver Brexit on time," Mrs May told the Commons.
But Labour leader Jeremy Corbyn said MPs were being "blackmailed into supporting a deeply flawed deal", calling it "an irresponsible act".
Are we running out of time?
By Daniel Kraemer, BBC Westminster
The prime minister's critics say she is just pretending to try to get changes to the deal she signed with the EU so she can push the final vote on it right down to the wire.
Labour's shadow Brexit secretary Sir Keir Starmer says what she actually intends to do is return to Parliament after the 21-22 March European Council summit, the week before Brexit, and offer MPs a "binary choice" - her deal or no deal.
Holding such a vote a few days before Britain leaves the EU might scare enough Labour MPs worried about a no-deal Brexit into backing the prime minister to get it through.
The government insists this is not its strategy and it will hold a "meaningful vote" as soon as it gets the changes to the deal it is seeking from Brussels.
Mr Corbyn said Mrs May was "merely engaged in the pretence of working across Parliament to find solutions", but she has "not indicated she will move one iota" on her red lines.
He told MPs: "We were promised a meaningful vote on a deal in December, it didn't happen. We were told to prepare for a further meaningful vote this week after the prime minister again promised to secure significant and legally binding changes to the backstop and that hasn't happened.
"Now the prime minister comes before the House with more excuses and more delays."
The SNP's leader at Westminster, Ian Blackford, was reprimanded by Commons Speaker John Bercow for shouting "liar" at the prime minister as she was making her statement.
Mr Blackford agreed to withdraw his remark "in deference" to the Speaker, but did not apologise to Mrs May. MPs are banned by Commons rules from calling other MPs liars in the chamber.
He said Mrs May was "lost in a Brexit fantasy", saying: "We're 45 days from Scotland being dragged out of the European Union against our will - 45 days from economic catastrophe."
Conservative MP Phillip Lee, who campaigns for another EU referendum, told the BBC he expected to see more ministerial resignations at the end of the month, when some of his colleagues "are going to have to make a stand and say: 'I'm sorry this is not acceptable'".
He said the promise of a further Commons vote on 27 February had taken the "fizz" out of Thursday's vote, which meant that the end of the month would "see some action from Conservatives in government".
Mrs May also set out plans to lift a requirement for a 21-day delay before any vote to approve an international treaty, in order to get a Brexit deal ratified in time for 29 March.
Former attorney general Dominic Grieve warned that time was running short for the ratification of a deal under the Constitutional Reform and Governance Act.
Mrs May said: "In most circumstances, that period may be important in order for this House to have an opportunity to study that agreement."
Brexit Secretary Stephen Barclay has, meanwhile, told senior European Parliament members that the UK requires legally-binding changes to the Irish backstop, but kept open the idea that these could be achieved without rewriting the text of the withdrawal agreement.
On a visit to the European Parliament in Strasbourg, Mr Barclay said he would continue working with EU chief negotiator Michel Barnier and he will call him after Thursday's Commons votes.
Foreign Secretary Jeremy Hunt met French foreign minister Jean-Yves Le Drian and Europe Minister Nathalie Loiseau earlier, in Paris.
Following the meetings, a French Foreign ministry statement said France "supports the planned withdrawal agreement" and added that it was "up to the British authorities to clarify their intentions".