EU leaders meeting in Brussels expressed their concern at the lack of progress in negotiations, exactly nine months before Britain leaves the bloc in March 2019.
"There's a great deal of work ahead and the most difficult tasks are still unresolved," Tusk told an end-of-summit press conference.
"This is the last call to lay the cards on the table."
Britain is hoping to agree a withdrawal deal and the outline terms of a future trading and security partnership by October, but talks have become stalled on the issue of the Irish border, Presstv reported.
The EU's chief negotiator Michel Barnier said he hoped a policy paper from London, due within weeks, would "contain workable and realistic proposals".
"But let me mention once again that time is very short. We want a deal and are working for a deal, but time is short," he said.
French President Emmanuel Macron added: "We can't wait any longer."
May attended the first day of summit and before leaving in the early hours of Friday, after all-night talks on migration, agreed negotiations must step up.
"We are ready to intensify and accelerate the pace of negotiations, I want to see that from the European Commission and the European Union as well," she said.
The summit was originally viewed as a crucial point in the Brexit process, but was sidelined due to the lack of progress and an EU row over irregular migration.
'No deal' preparations
In their summit conclusions, the other 27 leaders expressed "concern that no substantial progress has yet been achieved" on the Irish issue.
They called on member states "to step up their work on preparedness at all levels and for all outcomes".
Britain has said it expects a deal but is prepared to walk away from the talks if necessary -- although critics say it is ill-prepared for a no-deal scenario.
Dutch Prime Minister Mark Rutte said "all the efforts in the UK should be on finding a solution" on Ireland, "because that is holding up so many other issues".
All sides have pledged to avoid border checks between EU member Ireland and Northern Ireland, which is part of Britain, amid fears of the impact they could have on the fragile peace in the region.
But London has yet to explain how this can happen while sticking to its wish to leave the EU's customs union and single market, to fulfill eurosceptics' hopes of an independent trade policy.
Irish premier Leo Varadkar, who held a one-to-one meeting with May on the sidelines of the summit, warned Britain must be prepared to make compromises.
He knocked back an idea being floated by some British commentators that Britain might follow EU rules on goods but not on services or free movement of workers.
Allowing Britain to pick and choose in that way "would be the beginning of the end of single market", Varadkar told reporters.
He added: "I think there will be progress in the coming weeks because there has to be.
"Time is running out. It is in absolutely no one's interest that we end up in a no-deal scenario."
May has called for a bespoke trade deal with the EU after Brexit, but has yet to set out the details amid government in-fighting over how close to stay aligned.
She will gather her warring ministers at her country retreat at the end of next week to thrash out a deal and will publish her policy paper shortly afterwards.
In a letter to London's Evening Standard, former Brexit minister George Bridges urged his one-time colleagues to stop arguing.
"If you stay in your trenches, lobbing grenades at each other, the EU will be the winner," he said.