They've spent two days in Salzburg trying to do just that, but with things at a standstill, each side tried to ramp up pressure on the other.
Jacob Rees-Mogg, leader of the influential European Research Group of pro-Brexit Tories and a prominent critic of the Prime Minister's plan, summed up events in Salzburg by tweeting "Chequers goes pop" with the hashtag #ChuckChequers.
French President Emmanuel Macron said on Thursday the Brexit plan proposed by British Prime Minister's Theresa May was unacceptable in its current form and that he expected new proposals from Britain in October.
"Brexit is the choice of the British people pushed by those who predicted easy solutions".
In another blow to May's hopes of winning over European Union leaders, French president Emmanuel Macron told reporters that Brexit was a project which had been pursued by "liars".
"Taking the United Kingdom off the Brexit cliff edge without knowing where it lands would be the most irresponsible thing any prime minister has done in a very, very long time", she told the BBC.
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They can only be used to play Switch Online's exclusive library of classic NES games , such as Metroid , Super Mario Bros . Backups happen automatically after playing a game, but you will want to do an initial manual backup.
Austrian Chancellor Sebastian Kurz, who hosted the Salzburg summit, added that the European Union was "ready to compromise but we also expect that from the UK", calling for May to offer a "step forward".
Any Brexit deal will include a withdrawal agreement and transition period to smooth Britain's exit from the bloc. Neither side wants an arrangement that would require the rebuilding of border infrastructure, the removal of which was a key part of the Good Friday Agreement that brought peace to Northern Ireland after years of sectarian strife.
"What we want to avoid is any new barriers to the movement of goods, any new barriers to trade, any new barriers to the movement of people", Varadkar said.
'We once again reconfirmed our full unity, ' said European Council president Donald Tusk after Mrs May addressed the leaders.
On the issue of keeping the Northern Irish border open and "frictionless", to avoid a visible border that would risk reigniting old tensions, May said the UK's proposal was "the only serious and credibly proposition on the table for achieving that objective".
Speaking of May's proposals, Merkel said, "You can't belong to the single market if you are not part of the single market, but you can develop a lot of creativity to find practical, good, close solutions".
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After her briefing with Tusk, May told reporters there was still "willingness to do a deal" on both sides of the negotiation.
"Everybody shared the view that while there are positive elements in the Chequers proposal, the suggested framework for economic co-operation will not work, not least because it is undermining the single market", he said at the conclusion of the two-day meeting. He said that while there were "positive elements" in May's Chequers plan, a deal that puts the single market at risk can not be accepted.
If there is another referendum, however, British people living in other European Union countries for more than 15 years would be excluded from taking part again if the franchise is the same as last time.
But Mr Raab insisted it was "the most credible plan" for Brexit, challenging critics by saying it was "a bit late in the day" for alternative proposals.
'No deal is not my working assumption, ' said EU Commission president Jean-Claude Juncker. Parliament was very unlikely to support Chequers, it certainly will not allow more than Chequers.
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If Afghanistan does decide to go full strength today, our money is on them to emerge victorious against Bangladesh . However, it does not matter who tops the groups stage because all teams in Super Four will play against each other.