Theresa May and European Commission President Jean-Claude Juncker have said efforts to find an agreement in the Brexit talks should "accelerate" in the coming months.
Following talks in Brussels, the Prime Minister and Mr Juncker issued a joint statement describing their meeting as "constructive".
"The Prime Minister and the President of the European Commission reviewed the progress made in the Article 50 negotiations so far and agreed that these efforts should accelerate over the months to come," they said.
"The working dinner took place in a constructive and friendly atmosphere."
The meeting came after the EU's chief negotiator Michel Barnier warned last week that the discussions remained "deadlocked" over Britain's "divorce bill".
He made clear he could not recommend to other EU leaders that they were ready to move on to the second phase - including a free trade deal - when they meet in the Belgian capital on Thursday.
But while there were few details of the discussion between Mrs May and Mr Juncker, the upbeat tone of the statement will encourage hopes among British officials that the talks can make progress before the end of the year.
There has been intense frustration on the British side that Mr Barnier - who was also present with Brexit Secretary David Davis - has been unwilling to move forward until there is greater clarity on the so-called withdrawal issues, including the Irish border and future citizens' rights.
EU negotiators in turn have complained that while Mrs May promised in her Florence speech the UK would honour its outstanding financial obligations, Mr Davis has so far refused to put a figure on the proposed financial settlement.