Britain's Prime Minister Theresa May and European Council President Donald Tusk | Christian Hartmann/AFP via Getty Images Donald Tusk gives UK ‘absolute deadline’ to make Brexit offer The EU needs to see progress in 10 days, the European Council president said.

European Council President Donald Tusk set an “absolute deadline” of December 4 for the U.K. to submit a revised offer on the Brexit bill and a credible solution for the Irish border, telling U.K. Prime Minister Theresa May on Friday that otherwise it would not be possible to move on to the second phase of talks, a senior EU official said.

The official said May had accepted the timeframe, and that Tusk warned her if London misses the deadline, the European Council would not be able to declare “sufficient progress” at its December summit.

December 4 is also the night May is scheduled to have dinner with European Commission President Jean-Claude Juncker.

After a meeting with May in Brussels after an Eastern Partnership summit, Tusk said reaching sufficient progress on the three main divorce terms was "possible" but Brussels would "need to see progress from U.K. within 10 days on all issues, including on Ireland."

May, emerging from the meeting, repeated the lines from her Florence speech in September, in which she promised that the EU27 would not have to pay more in its current long-term budget cycle as a result of Brexit. And she repeated her assurance that the U.K. would meet its financial obligations.

"There are still issues across the various matters that we are negotiating on to be resolved but there’s been a very positive atmosphere in the talks and a genuine feeling that we want to move forward together,” she said.

But there was no indication that she had gone substantially further in her discussions with Tusk, or clarified the U.K.'s intentions in writing, as the EU has demanded.

An EU official said the hour-long meeting between Tusk and May included a frank discussion about the extremely tight timeline that the U.K. now faces, as well as the possibility that issues related to the Ireland border could be an even bigger stumbling block than the financial settlement.

“Particularly attention was on how to ensure the support of Ireland to move to the second stage,” the official said, adding: “The U.K. will need to give credible assurances as to how to avoid a hard border before 4 December, as it is still unclear how this can be done.”

Sufficient progress in #Brexit talks at December #EUCO is possible. But still a huge challenge.

We need to see progress from UK within 10 days on all issues, including on Ireland. pic.twitter.com/NKe86zGo17 — Donald Tusk (@eucopresident) November 24, 2017