Merkel, who eased tension at the start of the talks by sharing a joke with May over photographs of them both wearing very similar jackets, stressed a need for calm and order: "We want an orderly exit by Britain", she said.
European Union leaders gave Theresa May a new Brexit deadline of October 31, four months longer than the prime minister asked for, in a move the EU summit chair said would let Britain resolve its domestic deadlock on the issue.
Britain's Prime Minister Theresa May and Germany's Chancellor Angela Merkel look at a tablet next to European Council President Donald Tusk, ahead of a European Council meeting on Brexit at the Europa Building at the European Parliament in Brussels, Belgium April 10, 2019.
As Mrs May awaited the result of the European Union summit meeting at the British Ambassador's residence in Brussels, the senior Tory MP said: "I hate to say this but the reality is if we end up going and accepting a year-long, or even a nine-month extension, I think we're going to have egg all over our face".
Summit chair Donald Tusk and others argued that obliging May to accept a much longer deadline than the June 30 date she had sought could help swing pro-Brexit hardliners within her own Conservative party behind her deal, fearing a long delay could see the British public turning against a withdrawal altogether.
"What's indispensable is that nothing should compromise the European project in the months to come", he said.
European Union leaders have already agreed one delay to Brexit, from March 29 to April 12, and Tusk has warned there is "little reason to believe" the British parliament can ratify May's deal by June 30. The agreement has been rejected by Parliament three times and last week Ms.
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After six hours of sometimes fractious talks, European Union leaders settled on a compromise.
In contrast to some testy recent summits, there were signs of warmth and even humour.
May and German Chancellor Angela Merkel were filmed laughing over a tablet bearing an image showing the two of them speaking to their respective Parliaments on Wednesday wearing similar blue jackets.
He said it will field candidates drawn from the business world rather than career politicians, if the European Elections go ahead on 23 May, and it already had nearly 1,000 requests from people wanting to stand. Finally, if we failed to agree on any next extension, there would be a risk of an accidental no-deal Brexit.
"I take responsibility for this position, I think it's for the collective good".
In Luxembourg, EU affairs ministers discussed conditions for any long delay, which includes Britain holding European elections.
Despite the new agreement, May's future is uncertain. Many Conservative Party lawmakers would like her to quit now and let a new leader take charge of the next stage of Brexit.
Conversations between May's government and the opposition Labour Party are presently not close to breaking the Brexit deadlock, according to John McDonnell, a Labour Party politician.