A deal must be sealed soon so parliaments have time to give their verdict on it.
Underscoring the newfound sense of non-urgency, Prime Minister Sebastian Kurz of Austria, which holds the rotating EU presidency, even spoke of the "coming weeks and months" to get a deal and sought to impose a soothing calm.
"There's no need to dramatise matters. It's always the case with negotiations, that in the end there are challenges," Kurz said.
May addressed other EU leaders before they gathered for a dinner of pan-fried mushrooms and turbot in wheat beer — without her — to assess the state of Brexit talks.
May urged her counterparts to redouble efforts to find the way to a deal, but European Parliament President Antonio Tajani said she did not offer them concrete new proposals.
"Politically speaking, a will was expressed to move forward and reach agreement but there was nothing substantively new in terms of content," Tajani told reporters.
May spoke a day after Tusk implored her to present new ideas for resolving the tricky problem of how to keep the land border between the Republic of Ireland and the UK's Northern Ireland friction-free once Britain no longer is an EU member.
Tusk advised May that "creative" thinking from Britain was required to avoid a hard border on the island of Ireland, the issue that has brought Brexit negotiations to a standstill.
Both sides agree there must be no hard border, but each has rejected the other side's solution.
At present the two sides are proposing that Britain remains inside the EU single market and is still bound by its rules from the time it leaves the bloc in March until December 2020, to give time for new trade relations to be set up.
Many suspect that will not be enough time, which has led the EU to demand a "backstop" to ensure there are no customs posts or other controls along the currently invisible border between Northern Ireland and Ireland.
EU leaders have recently suggested that the transition period, currently due to end in December 2020, could be extended by a year to provide more time for a trade deal to be forged that would make the backstop unnecessary.
Britain says it has not asked for an extension — but didn't rule it out today.
The summit in Brussels had long been seen as the "moment of truth" in the two-year Brexit process. But after urgent talks on the Irish border ended on Monday without producing a breakthrough, today's gathering looked more like a therapeutic bonding session than an occasion to celebrate.
The timeline for a deal has slipped into November, or even December, when another EU summit is scheduled.
The summit continues tomorrow with an agenda limited to some issues both sides firmly agree on, including fighting cybercrime and dealing with an assertive Russia.
May and other EU leaders all expressed cautious optimism that an agreement could be achieved in time to avoid an economically disruptive "no-deal" Brexit in March.
But persuading the bloc is only part of the British leader's problem. She will have to get any deal past her Conservative Party — split between "hard" and "soft" Brexit factions — and past her parliamentary allies in Northern Ireland's Democratic Unionist Party, who insist a solution can't include customs checks between Northern Ireland and the rest of the UK.
It must also be approved by Britain's Parliament, where May lacks an overall majority.
Lithuanian President Dalia Grybauskaite said that Britain had still not explained clearly how it wants to leave the EU.
"Today, we do not know what they want," she said. "They do not know themselves what they really want. That is the problem."
- AP
