Theresa May is to hold last-minute Brexit talks with the leaders of Germany and France later, four days before the UK is due to leave the EU.
Mrs May is meeting Angela Merkel in Berlin, followed by Emmanuel Macron in Paris, to urge them to back her request to delay Brexit again until 30 June.
The prime minister will be at an emergency summit on Wednesday when all EU states will vote on an extension.
Cross-party talks aimed at breaking the impasse are also set to continue.
The negotiating teams will be joined by Chancellor Philip Hammond and shadow chancellor John McDonnell, with the Labour frontbencher saying they hoped to “broaden the talks”.
The UK is currently due to leave the EU at 23:00 BST on Friday.
So far, MPs have rejected the withdrawal agreement Theresa May reached with other European leaders last year.
One of most contentious parts of the plan is the Irish backstop – an insurance policy that aims to prevent a hard border returning to the island of Ireland.
The EU has continually said it will not re-open the withdrawal agreement for negotiations, but Leader of the Commons Andrea Leadsom renewed her plea for them to look again.
She told reporters the “best possible outcome” would be if the “EU decide to support measures on the backstop”, and that she though it would be “fantastic [if] Angela Merkel will try to support a proper UK Brexit by agreeing to open the withdrawal agreement”.
But speaking at a press conference in Luxembourg on Tuesday morning, the EU’s chief negotiator, Michel Barnier, said: “The withdrawal agreement is not going to be reopened. It is not up for negotiation again.”
On Monday evening, Parliament passed a bill brought by Labour MP Yvette Cooper, which aims to force the prime minister to request a Brexit extension – rather than leave the EU without a deal on Friday, which is the default position.
The government opposed the bill, saying it was unnecessary as Mrs May was already seeking an extension. But the backbenchers behind it wanted to ensure it became law to prevent any changes in her strategy.
As a result, there will be a government motion on Tuesday asking MPs to approve the PM’s request to the EU to delay Brexit.
The final decision on an extension lies with the EU – and the leaders of all the 27 other EU countries have to decide whether to grant or reject an extension.
If the UK is still a member of the EU on 23 May, it will have to take part in European Parliamentary elections.
Germany’s Europe Minister Michael Roth said Mrs May would receive a warm welcome in Berlin, but his government’s priority was maintaining the unity of the European Union.
On Monday, Mrs May spoke by phone to the Dutch Prime Minister Mark Rutte, who said it was “crucial” for the EU’s members to know “when and on what basis” the UK will ratify the withdrawal deal.
Luxembourg’s Foreign Minister Jean Asselborn said the UK would “certainly not” leave without a deal on Friday.
But Ireland’s Deputy Prime Minister Simon Coveney said a no-deal Brexit was still possible – even though it would represent “an extraordinary failure of politics”.