The European Union will also have to make compromises if a Brexit trade deal is to be signed, Angela Merkel has said.
In a rare intervention aimed at cooling tensions over stalling negotiations, the German chancellor said it would not just be down to the UK to change its position.
Her comments come after EU leaders issued a statement saying it was for the UK to “make the necessary moves to make an agreement possible” – angering the government in London.
UK chief negotiator David Frost on Thursday night said he was "disappointed" at the tone struck by the European Council, and "surprised" by the suggestion that to get an agreement "all future moves must come from UK".
Lord Frost, who was recently enobled by Boris Johnson, said the EU's statement was "an unusual approach to conducting a negotiation".
Boris Johnson is set to make a decision later on Friday about whether to accept an offer by the EU to extend talks until the end of the month. The PM had previously said today's summit was his final deadline and that there was little point in talking about the issue into the autumn – but has since suggested the decision has not yet been made on whether to walk out.
Speaking on the doorstep of the Thursday and Friday summit, Ms Merkel told reporters: “In some places things have moved well, in other places there is still a lot of work to be done.
“We have asked the United Kingdom to remain open to compromise, so that an agreement can be reached. This of course means that we, too, will need to make compromises.”
The three major intractable issues remaining are the question of fishing rights, governance, and a level playing field in regulations, particularly around state aid.
Of these, fishing has seen the least progress, though EU chief negotiator Michel Barnier has previously hinted the EU is willing to compromise.
The issue is politically difficult in a number of member states whose coastal communities rely on fishing in British waters, however. Of these, France is the most outspoken - with president Emmanuel Macron saying at the start of the summit that he would not sacrifice French fishermen for Brexit.
Belgian prime minister Alexander De Croo late on Thursday night summarised the view of many leaders on the European Council, telling reporters: "Letting ourselves be put under pressure by time and then making mistakes in a deal which in the long run could be really, really difficult for European business is something we should not do.
"I agree it would be crazy not to have a deal, but it would be even more crazy to have a bad deal."