EU leaders have dismissed talk of renegotiating the draft Brexit deal and warned the UK's political situation could make a "no-deal" more likely.
German Chancellor Angela Merkel said there was "no question" of reopening talks as a document was "on the table".
Meanwhile French PM Edouard Philippe said there was a need to prepare for a no-deal because of UK "uncertainty".
The EU has set out a series of meetings leading up to 25 November when it plans to approve the Brexit agreement.
However leaders admit that there is still much ground to cover after the UK Prime Minister Theresa May won backing on Wednesday from her cabinet for the 585-page draft agreement.
"We still have a long road ahead of us on both sides," the EU's chief Brexit negotiator Michel Barnier said.
On Thursday, Mrs Merkel said she was pleased that progress had been made.
But following news of
resignations from Mrs May's cabinet, including the UK's Brexit Secretary Dominic Raab, she said it was possible that Britain may still leave without a deal.
She also said that there was no appetite for further talks on possible amendments to the current agreement.
"We have a document on the table that Britain and the EU 27 have agreed to, so for me there is no question at the moment whether we negotiate further," she said.
Mr Philippe appeared to echo her sentiment over UK political uncertainty.
"It will escape no-one that the current political situation in Britain could fuel uncertainty... over the ratification of the accord," he said.
How have other European leaders reacted?
The European Parliament's Brexit chief Guy Verhofstadt said the deal had been hammered out after two years of "intense negotiations" and he hoped UK MPs would accept that "there is not a lot of room [for] manoeuvre to say, 'OK, let's start again'".
French Finance Minister Bruno Le Maire said the deal was "good news for the French economy" but also issued caution, saying the UK must be made to respect all EU rules.
Finland's Prime Minister Juha Sipila tweeted to say that while Wednesday's developments were important, "decisions on both sides are still needed for a final agreement".
Austrian Chancellor Sebastian Kurz said he was "very pleased" and "optimistic", adding: "We are pinning our hopes on it."
What has the EU said and what happens next?
Speaking on Thursday alongside EU Council head Donald Tusk, Mr Barnier said the agreement was fair and balanced, took into account the UK's needs and laid the ground for an "ambitious new partnership".
Mr Tusk praised Mr Barnier's work and said the agreement had "secured the interests of the 27 member states and EU as a whole".
He laid out the timetable for the days ahead.
- EU member states will analyse the document and at the end of the week national envoys will share their assessments
- A political declaration on future ties between the EU and the UK will be agreed by Tuesday and members will have 48 hours to evaluate it
- The EU Council will then meet for a summit on 25 November to finalise the agreement "if nothing extraordinary happens", Mr Tusk said. The leaders of the 27 EU nations must approve the deal
Mr Tusk said: "Since the very beginning, we have had no doubt that Brexit is a lose-lose situation, and that our negotiations are only about damage control."
Addressing the UK, he added: "As much as I am sad to see you leave, I will do everything to make this farewell the least painful possible, for you and for us."
Mr Barnier later took the document to the European Parliament. Its president, Antonio Tajani, said MEPs would vote on the deal in early 2019.
If the agreement is approved by both sides, a 21-month transition period will kick in, during which a trade deal and the thorny issue of how to ensure there is no physical border between Northern Ireland - part of the UK - and the Republic of Ireland will need to be worked out.
A smooth border-free exchange underpins the peace deal that ended the Northern Ireland conflict.
Volatile UK politics could bin Brexit deal, worries EU
K
atya Adler
Ashen-faced European diplomats haunt the corridors of Brussels. No rest for them until Sunday 25 November - the day of the "seal the deal" Brexit summit between Theresa May and EU leaders.
So what do they have to do between now and then?
Diplomats from the 27 EU countries must now pore over 585 pages of the draft Brexit withdrawal agreement with lawyers to ensure all will be to each government's liking.
If a problem is identified, it will need to be transmitted to the team of Michel Barnier, the EU's chief Brexit negotiator, as early as this Friday or Saturday.
The 27 member states (and Theresa May) also still have to agree what should be in the political declaration on the future EU-UK relationship.
This part of the divorce treaty is not legally binding - but it is symbolically important. At the moment the text is solely made up of a series of bullet points and headings. So the pressure is definitely on, leading up to the 25th.
But all this could be in vain if the Brexit deal is voted down by the UK parliament in a few weeks' time.
The EU knows this is a very real possibility.
I put the question to Michel Barnier on Wednesday night at his press conference - but, skilled politician that he is, he refused to engage.
Brussels is very keen indeed not to give the impression that the EU might change or come up with a "better" Brexit deal text if this one ends up being rejected in the House of Commons.
Mr Barnier quoted Theresa May as saying that this is a deal in the UK's interest.
In fact, he spoke so warmly about the deal - how hard EU and UK negotiators had worked on it, how successful they had been in protecting citizens' rights, the Irish border and the constitutional integrity of the UK - that one colleague commented to me it was as if Mr Barnier, known for his suave French manner, believed they had managed to conjure an exquisitely designed Faberge egg out of the complex Brexit process.
No wonder then that he didn't want to engage in the possibility of that egg getting smashed.
Truth be told, he's unlikely to face much trouble from the EU side.
He is off to Strasbourg on Thursday to schmooze the European parliament - which has a veto over the Brexit deal.
MEPs will look at the section of the withdrawal agreement on citizens' right with a particularly critical eye as that is the issue they tend most to focus on. But Mr Barnier has been careful to keep the parliament in the loop on negotiations throughout, so they're unlikely to reject a final agreement.
EU countries had also given Ireland an effective veto over the deal if Dublin were unhappy about the provisions for the Irish border.
But the Irish prime minister gave the green light to the draft text on Wednesday, so that is no longer an issue.
Spain and Gibraltar, and Cyprus and the UK military bases on the island were also thought to be potential pitfalls. The withdrawal agreement sorted them out too.
This leaves the concerns the UK's biggest EU trade partners (like France and Germany) had over the so-called "level playing field": ensuring that the UK was tied to extra EU regulations in the temporary customs relationship outlined in the Irish backstop, should it one day be triggered.
Well, about 100 pages of the draft withdrawal treaty are dedicated to these extra ties - on state aid, environment and labour regulations - ensuring that UK business should not have a competitive advantage over EU ones in a customs partnership.
Rights to fish in UK waters after Brexit have not yet been agreed, and the Spanish, French, Danish or Dutch will probably have something to say about that - but it's not a deal breaker at this stage.
So, those Europeans wary of political trouble that could disrupt or destroy the careful Brexit deal choreography between now and 25 November (and beyond) look fearfully at the politically volatile UK.
This led one EU civil servant late on Wednesday night to jab at the 585 pages of the draft Brexit treaty, muttering: "You know what? All this could still end up in the bin."