May capped a day of diplomacy by dining with Juncker at EU headquarters in Brussels on Monday. The two leaders said in a joint statement their meeting "took place in a constructive and friendly atmosphere" and both stressed the urgent need for progress in the Brexit talks.
EU and U.K. officials have exchanged some spiteful words in recent weeks over the pace and substance of the negotiations. The British government wants to start discussing the country's post-departure relationship with the EU.
The EU has maintained there has been insufficient progress on such issues as the rights of EU citizens already living in Britain.
The President of the European Commission refused to divulge what issues he would discuss with British Prime Minister Theresa May over dinner on Monday and said to wait until "the autopsy."
EU officials said that the meeting would span much more than the struggling Brexit talks to include current trade relations with global partners, but since both will also bring their chief negotiator for the talks, the stalemate in the negotiations will be on the agenda.
EU Commission President Jean-Claude Juncker said: "I will see Mrs. May this evening. We will have discussions and then you will have the autopsy."
British Foreign Secretary Boris Johnson is urging the European Union to speed up Brexit talks and start discussing now their future relationship after the U.K leaves in 2019.
Johnson said in Luxembourg on Monday: "Let's get these conversations going and stop letting the grass grow under our feet."
He said it's time for "the great ship to go down the slipway and onto the open sea and for us to start some serious conversations about the future and the new relationship."
Johnson's remarks came ahead of a Monday dinner meeting between Prime Minister Theresa May, European Commission President Jean-Claude Juncker and top Brexit negotiators.
EU leaders are expected this week to rule that not enough progress has been made for the negotiations to be expanded to include future relations and trade.
U.K. Prime Minister Theresa May is heading to Brussels to meet with senior European Union officials in hopes of reinvigorating stalled negotiations on Britain's departure from the European Union.
May's unexpected decision to meet European Commission President Jean-Claude Juncker and chief negotiator Michel Barnier follows Barnier's comment last week that the latest round of talks had ended in a "disturbing deadlock" over Britain's financial obligations.
EU estimates suggest Britain's divorce bill could range from 60 billion euros to 100 billion euros ($80 billion to $120 billion). Britain has rejected such figures.
EU leaders are demanding progress on the divorce bill, the rights of citizens hit by Brexit and the border between the Republic of Ireland and Northern Ireland before talks can move on to issues such as future trading arrangements.