Theresa May will meet EU officials later as the two sides scramble to finalise a Brexit deal in time for Sunday’s summit of European leaders.
The EU missed its deadline on Tuesday to complete the text of its declaration on future relations with the UK, amid concerns from several member states.
Stumbling blocks remain over UK access to the EU single market, access to UK waters for EU boats and Gibraltar.
The PM is under pressure from her own MPs not to give any further ground.
It comes as the new work and pensions secretary Amber Rudd appeared to rule out the option of a no-deal Brexit.
She told BBC Radio 4’s Today programme: “It’s my view that parliament, the House of Commons, will stop no deal. There isn’t a majority in the House of Commons for that to take place.”
The BBC’s Norman Smith said Ms Rudd’s stance appeared to be at odds with the prime minister, who has warned that if her deal is voted down by MPs there will either be no deal or “no Brexit”.
Mrs May has also repeatedly warned that she believes that “no deal is better than a bad deal”.
Asked on Today if she would back another referendum, like some of her fellow Remain-voting Tory MPs on the backbenches, Ms Rudd said: “I don’t think we are looking at another referendum.”
She said MPs would “take a careful look over the abyss” and decide it was in the “best interests of the country” to vote for Theresa May’s Brexit withdrawal agreement.
She later added that she had come to this view “having spent the past six to seven months on the backbenches talking to various other backbenchers”.
But she denied she was at odds with the prime minister, saying: “Well, there’s deal, there’s no deal, there’s no Brexit. There’s three ways this can go. I’ve given you my view.”
Labour’s shadow Brexit secretary Sir Keir Starmer said: “Amber Rudd seems to have ignored Number 10’s spin by admitting that Parliament would stop a no-deal Brexit.
“If the prime minister’s deal is rejected then MPs will not sit back and allow us to crash out of the EU without an agreement. Parliament will take back control.
“After these comments from Amber Rudd, it’s time for the government to drop the false choice between a bad deal and no deal, and to come forward with a plan that can command the majority support of Parliament.”
Mrs May appears to have faced down the threat of a challenge to her position from Brexiteer critics of the deal, for the time being at least.
However, Tory MPs unhappy with Mrs May’s handling of Brexit negotiations want much more clarity on the terms of the UK’s future co-operation with the EU if they are to back the final deal – which will be put before European leaders this weekend.
All sides in the Commons have warned of a “blind Brexit” in which the UK signs up to a series of legally-binding commitments in the draft withdrawal agreement, without similar guarantees over future trading arrangements.
The withdrawal deal was agreed in principle by both Mrs May and the EU last week. It includes a £39bn “divorce bill” and the controversial customs “backstop” which keeps the UK temporarily in the EU customs union as a way of preventing the return of manned customs posts at the Irish border.
However, the joint political declaration on future relations – still being drafted – would only set out the shape of the UK’s trading relationship with the remaining 27-nation bloc, without any legal commitments.
Any binding trade deal would still have to be thrashed out in the 21-month transition period after Britain leaves the EU on 29 March 2019.
The BBC’s political editor Laura Kuenssberg said some UK ministers still believed there was time for a few “nips and tucks” to the withdrawal agreement reached in principle last week.
During a flying visit to Brussels designed to prepare the ground for this weekend’s summit of EU leaders, Mrs May will hold talks with European Commission president Jean-Claude Juncker.
The prime minister departs for Brussels with her position seeming more secure, despite a week of cabinet resignations and political plotting to remove her from post.
On Tuesday one of Mrs May’s most ardent critics, Jacob Rees-Mogg, said the time “is now” for fellow backbenchers to either force a confidence vote in Mrs May or have her lead the party into the next election.
But he accepted it could be next month before the required threshold of 48 letters needed to trigger a contest was reached.
The prime minister’s allies insist she would win any confidence vote, with party rules meaning she would then be immune from a challenge for 12 months.
And a YouGov poll commissioned by the Times suggests that 46% of voters backed Mrs May staying in post, against just 33% a week ago.
Why is May rushing to Brussels?
By Katya Adler, BBC Europe editor
Could this all be more about optics than nitty-gritty politics?
Grumbling aside, no-one in European circles seriously thinks any EU country will refuse to sign up to the Brexit deal by end of play this weekend.
They’re all keen to avoid a no-deal scenario and they want to help Theresa May get the Brexit texts through a vote in the House of Commons.
Engaging in last-minute political fisticuffs with the EU is arguably advantageous for Mrs May.
A high-drama, climactic Brexit summit ending in a (presumably planned) late night/early morning bleary-eyed but triumphant resolution with EU leaders would allow the prime minister to claim that the final text of the deal was hard fought and hard won… in the fervent hope that will soften the stance of some of her many critics at home.
Discussions in Brussels focus on the political declaration outlining relations from the scheduled end of the transition period in 2021. Currently running to 20 pages, it will sit alongside the withdrawal agreement.
The BBC understands the intention is still to present a completed text to leaders at Sunday’s summit but opinions differ over how easy it would be to solve the outstanding issues.
Spain has warned it will reject the draft Brexit withdrawal deal without a clarification of the text on future talks on the status of Gibraltar.
Spain maintains a claim to the peninsula, ceded to the British crown under the 1713 Treaty of Utrecht and it wants to ensure that future EU talks with the UK do not cover Gibraltar.
Ambassadors from the EU’s 27 remaining countries had been due to be briefed on the final text on Tuesday but the meeting has been re-scheduled for later this week.