But a drive by Macron to keep London on a tight leash with an extension no longer than to June saw the emergency summit bogged down in late-night wrangling as German Chancellor Angela Merkel and others argued the merits of granting up to a year.
Over a dinner of scallop salad, cod loin and macadamia nut parfait, it soon emerged that France was almost isolated, with only a handful of member states, such as Belgium, sounding sympathetic to his arguments.
French pressure also tightened clauses referring to Britain not disrupting European Union affairs if it stays in longer and a reference to a June 20-21 European Union summit taking stock of the position again.
German officials were said to be "very irritated" with Macron.
"We would be generous in negotiating that, understanding that the United Kingdom couldn't be a silent partner in such an arrangement - it would have to have a say in decisions being made", Irish premier Leo Varadkar said as he arrived at the summit.
"Nothing is decided", Macron said, insisting on "clarity" from May about what Britain wants.
"At this stage, in my view, nothing should be taken for granted", Macron told reporters upon his arrival in Brussels.
"Putting in danger the functioning of Europe is not preferable to a no deal".
And if the European Council did not agree on an extension at all, "there would be a risk of an accidental no-deal Brexit", he said.
That would allow tariff-free trade in goods with the European Union but limit the United Kingdom from striking its own deals.More news: One step closer to football season! Browns release preseason schedule
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Michael Brown said he has become so fed up with the Tories, he has now joined Nigel Farage's Brexit Party in anticipation of the United Kingdom taking part in the European elections.
They will then meet for dinner without her to agree a response to the UK's extension request. "We would have made a decision to weaken our institutions, by having a member who is permanently there but leaving". "But it was not logical in my view, and above all, it was neither good for us, nor for the United Kingdom", he said.
"This is why I believe we should also discuss an alternative, longer extension".
"What's indispensable is that nothing should compromise the European project in the months to come", he said.
Leader of the Brexit Party and MEP Nigel Farage speaks to the press inside the EU Council headquarters in Brussels.
Any Brexit delay does not mean talks will reopen between the United Kingdom and the EU.
An EU diplomat described the review clause as "nonsense" because as a member state the United Kingdom would have the right to veto any attempt to kick it out of the union.
EU leaders will gather for talks with European Parliament president Antonio Tajani on Wednesday evening, before hearing from Mrs May.
The agreement gives May more than the three months to June 30 that she asked for to build a parliamentary majority behind the withdrawal treaty she negotiated with the European Union previous year.
Some in the room found her presentation "credible and honest". The last time, May spoke for over an hour and took questions while the leaders discussed for about 5 hours.