But she insisted Britain could still secure a deal and leave before Britons would have to vote in a May 23-26 election to the European Parliament - a condition for the country to remain a member of the bloc beyond June 1 under the EU's accord.
'A long extension, without any rationale for how it is needed in order to deliver the UK's exit from the European Union, is simply not something to which the Prime Minister can lawfully agree.
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 a year ago.
Some were sympathetic, but French President Emmanuel Macron struck a warning note.
"We will shape this extension in such a way that, whenever Britain has approved the Withdrawal Agreement, Britain can then complete its orderly withdrawal very shortly after", she told German MPs.
The EU's chief Brexit negotiator, Barnier, speaking to the media when he arrived earlier said any article 50 extension would have to be "useful" and "serve a purpose".
The EU has continually said it will not re-open the withdrawal agreement for negotiations, but Leader of the Commons Andrea Leadsom has renewed her plea for it to look at it again.
In contrast to some testy recent summits, there were signs of warmth and even humour.
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At various times over the last several years as Baylor's seasons ended in disappointment, Mulkey tried to be philosophical. She said she doesn't know much about her injury but that she'll "get it fixed, whatever it is".
May signaled she would accept a longer extension, as long as it contained a get-out-early cause should Britain end its Brexit impasse.
If Britain does not elect European Union lawmakers, it must leave, with or without a deal, on June 1, according to a draft summit agreement seen by Reuters.
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.
The Netherlands and the Czech Republic preferred a longer postponement, saying it could scare staunch Brexit supporters in Britain into backing the exit deal over fear their project might never materialize at all.
"What is important is that any extension enables us to leave at the point at which we ratify the withdrawal agreement, " May said as she arrived in Brussels.
Macron is concerned that letting Britain stay too long would distract the EU from other issues - notably next month's European Parliament elections.
"The no-deal situation is a real option", said the official, who was not authorised to be publicly named according to presidential policy.She has tried four times before and each time it has been rejected.
He said if European elections take place in the United Kingdom because of a delay to Brexit "it's going to be a pretty farcical situation" and that many Conservative Party members would be "reluctant to participate" in the vote. Several days of talks between May's Conservative government and the main opposition Labour Party aimed at finding a compromise have failed to produce a breakthrough.
And he left fellow panellists on Iain Dale's Cross Question in absolute stitches with his criticisms of the Tories, Theresa May and her government. Labour favours a softer Brexit than the government has proposed, and wants to retain a close economic relationship with the bloc.