File photo by Daniel Leal-Olivas/AFP
Under pressure from all sides since losing her parliamentary majority in the June 8 vote, May held out an apparent olive branch on the uncertain fate of 3 million Europeans living in Britain.
German Chancellor Angela Merkel said the plans were a "good start", but added that "there are still many, many other questions" to be dealt with over Brexit.
Merkel had earlier made clear that Britain's exit was not at the top of the agenda for the remaining 27 EU members, as they try to capitalize on a renewed sense of optimism to put the bloc back on track after years of austerity and crisis.
The EU sought instead to show its unity by pressing ahead with plans on counter-terrorism, defense and by renewing damaging economic sanctions against Russia over the war in eastern Ukraine.
"For me the shaping of the future of the 27 is a priority coming before the issue of the negotiations with Britain on the exit," said Merkel, Europe's most powerful leader.
New French President Emmanuel Macron, attending his first summit, added that the EU had to "establish our own strategy based on our own interests".
May makes 'clear commitment'
A year after its shock referendum vote to leave the EU, Britain is mired in crisis. May's weakened position has raised fresh questions about whether her plan to leave the European single market will proceed.
Over dinner at the summit, May addressed the issue of citizens' rights, one of the key 3 priorities for the opening stage of Brexit negotiations that began on Monday, June 19.
No EU citizen currently in Britain would be asked to leave on Brexit day, she said, while EU citizens living in Britain for more than 5 years will get "settled status".
"The UK's position represents a fair and serious offer and one aimed at giving as much certainty as possible to citizens who have settled in the UK," May told her colleagues.
The prime minister said she expected any offer by Britain to be matched by the EU for the one million Britons living on the continent, a government source said.
But her proposal sets up a clash with the EU after she rejected Brussels's demand that the European Court of Justice oversee and resolve any dispute over citizens' rights post-Brexit.
May said the pledge on EU citizens would instead "be enshrined in UK law and enforceable through our highly respected courts".
She also drew criticism from a campaign group of EU citizens, the3million, which called her offer "pathetic".
"It fails on several points which would enable EU citizens in the UK to continue to live normally after Brexit," it said.
Other crunch Brexit issues are Britain's estimated 100 billion euro (88 billion pounds, $112 billion) divorce bill, and Northern Ireland, which will be on Britain's only land border with the EU after Brexit.
Imagine there's no Brexit
Earlier, EU President Donald Tusk had channelled John Lennon's "Imagine" as he said he hoped Brexit could be reversed – though others immediately poured cold water on the idea.
"Who knows? You may say I am a dreamer, but I am not the only one," the former Polish premier said with a broad smile, quoting Lennon's iconic song.
But Belgian Prime Minister Charles Michel – who has strongly argued for EU unity on Brexit – said Tusk should let it be.
"I am not a dreamer and I am not the only one," Michel told reporters, saying he thought it was "British humor" by Tusk.
Tusk said the EU had turned a corner in the year since the Brexit vote, adding: "Never before have I had such a strong belief that things are going in a better direction."
But the stage was later set for a possible row over the future of the European Banking Authority (EBA) and the European Medicines Agency (EMA), which will be relocated from Britain after Brexit.
The 27 EU leaders without May agreed to decide the future of the regulatory bodies, which bring both money and prestige, by November.
Law to combat online terror
In Brussels, security was stepped up after the failed bomb attack on Tuesday, June 20, at one of the city's main rail stations by an Islamic State sympathizer, following strikes in Britain and France.
EU leaders on Thursday urged Internet firms to do "whatever is necessary" to combat online extremism promoting such attacks, warning governments were ready to legislate if they did not act.
They also endorsed the EU's growing efforts to build up defense capabilities, especially amid concerns about US President Donald Trump's commitment to transatlantic ties.
And they recommended another 6-month rollover of tough economic sanctions imposed against Russia in 2014 over the conflict in eastern Ukraine, which has claimed 10,000 lives. – Rappler.com