Theresa May has been told by Europe's leaders it is the "last call" for her to set out her Brexit plans if she hopes to achieve a deal with the EU on the UK's future relationship in October.
Europe's leaders demanded clarity from Mrs May as their impatience over the Prime Minister's divided Cabinet became clear.
The leaders of the remaining 27 European Union nations issued a joint call for "realistic and workable" proposals from the Prime Minister.
At the close of a summit in Brussels, European Council President Donald Tusk said there was a "great deal of work ahead" on Brexit and the "most difficult tasks are still unresolved".
He said "quick progress" was needed in order to reach a deal at the October summit and "this is the last call to lay the cards on the table".
French President Emmanuel Macron said the remaining 27 EU member states "can no longer wait" for progress on Brexit.
Belgian Prime Minister Charles Michel pointed to Mrs May's domestic political difficulties, saying the British gave the impression of negotiating with each other, rather than the EU.
Brussels' chief Brexit negotiator Michel Barnier also warned that time was short and suggested an extra round of negotiations on Monday to help reinvigorate the talks.
Mr Barnier said "huge and serious divergence" remained over issues relating to Ireland and Northern Ireland.
The Prime Minister said she hoped a new phase in the Brexit talks would be possible after the publication of the Government's White Paper calling for negotiations to speed up and intensify once the document is published.
Details of the White Paper setting out the UK's plans for issues including trade and customs are expected to be thrashed out by Cabinet ministers at next Friday's Chequers away-day.
Mrs May's participation in the European Council summit ended in the early hours of Friday morning after a marathon session on proposals to address the migrant crisis.
Leaving the summit in Brussels, she said: "We are going to be publishing our White Paper shortly and I want to see the negotiations accelerating and intensifying thereafter."
Asked whether the White Paper would provide "realistic and workable" proposals, a Downing Street spokeswoman said: "Yes."
The Prime Minister is expected to meet key players in Europe in an effort to boost support for the White Paper, with Germany's Angela Merkel confirming she was expecting a visit from Mrs May.
The 27 remaining EU leaders swiftly agreed a joint position on Brexit in Mrs May's absence on Friday.
Maltese Prime Minister Joseph Muscat said the conclusions were agreed in under 60 seconds - the only straightforward decision made during a difficult summit for European unity.
The EU27 welcomed progress on the legal text of the withdrawal agreement but noted that "important aspects still need to be agreed" including the territorial application of the deal "notably as regards Gibraltar" - a provision thought to have been inserted at the insistence of Spain.
The 27 leaders also expressed concern that "no substantial progress has yet been achieved on agreeing a backstop solution for Ireland/Northern Ireland".
They demanded "further clarity as well as realistic and workable proposals from the UK as regards its position on the future relationship".
And in a hint that red lines could be softened, the 27 leaders said "if the UK positions were to evolve" the EU "will be prepared to reconsider its offer".
In a sign that "no deal" was still a potential outcome, the leaders called on member states and EU institutions "to step up their work on preparedness at all levels and for all outcomes".
The leaders of the EU27 had returned to the summit following a stormy working dinner on Thursday evening which stretched into the early hours of Friday as desperate attempts were made to find a compromise on migration.
Confirmation that a deal had been reached only came shortly after 4.30am local time when Mr Tusk tweeted conclusions had been agreed.
The issue has assumed greater political significance in Europe because of the threat to Mrs Merkel's position over her approach to letting migrants settle in her country.
Meanwhile, Italy's Giuseppe Conte used the summit to demand a fundamental change in the bloc's migration policy, saying his country received little help even though it was at the forefront of receiving migrants from across the Mediterranean.
Mr Tusk acknowledged it was "far too early to talk about a success" in terms of the EU migration package.
The vaguely-defined deal involves the creation of "regional disembarkation platforms" - facilities outside the EU where migrants picked up by search and rescue missions would be assessed to decide whether they are refugees or risking the Mediterranean crossing for economic reasons.
Within EU territory, those who are saved could be taken to "controlled centres" set up in member states for processing.