May hosted Juncker and chief European Union negotiator Michel Barnier for dinner at her Downing Street official residence, which her aides said was an attempt to improve the atmosphere before Brexit talks start in earnest in early June.
The EU wants the terms of the UK's exit to be decided before any discussion of a future trade relationship while Mrs May wants to the two issues to be dealt with simultaneously.
European Union leaders, without May, are scheduled to gather in Brussels on Saturday to agree on Brussels' negotiation guidelines.
Speaking at a conference in Thailand, he said "of course we accept some liabilities for this membership we've had for 40 years, just as we have a claim on some of the assets that we've paid into".
Heidrick & Struggles International, Inc. Earnings Ahead: Quick Glance
Wall Street is only getting more bullish on the stock, with 3 of analysts who cover IVAC having a buy-equivalent rating. The business earned $159.80 million during the quarter, compared to analysts' expectations of $146.14 million.
Senior members of the Government have insisted that Britain will not pay a bill of the scale suggested by the likes of Mr Juncker, with International Trade Secretary Liam Fox branding the idea "absurd".
France has warned Britain that the City must continue to be overseen by European regulators after Brexit and financial services could be excluded from any trade deal.
Brexit Secretary David Davis said "cool heads, strong leadership and traditional British resolve" would be needed to secure a good deal as the United Kingdom leaves the EU.
Negotiations between Britain and the bloc are due to start after the United Kingdom election, with the size of the divorce bill facing Britain one of the first thorny items on the agenda.
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