Britain has still not proposed any workable alternatives to the backstop in the Brexit Withdrawal Agreement, according to the European Union.
It comes following talks between European Commission President Jean-Claude Juncker and British Prime Minister Boris Johnson.
Mr Juncker used the meeting in Luxembourg to underline "that it is the UK's responsibility to come forward with legally operational solutions" if it wants to do away with the backstop, adding that "such proposals have not yet been made".
In a statement following the meeting, a spokesperson for Mr Juncker said that he underlined to Mr Johnson the European Commission's "continued willingness and openness to examine whether such proposals meet the objectives of the backstop. Such proposals have not yet been made".
It was the first face-to-face Brexit discussions between the two leaders since Mr Johnson became British prime minister.
They posed for photos before entering Le Bouquet Garni restaurant in Luxembourg for a working lunch.
Outside, Mr Johnson was asked if he was optimistic about the talks. "Cautious, cautious," he told reporters.
Mr Juncker was asked if he was confident of progress as he entered. "We will see," he replied.
Following the meeting, Mr Johnson skipped a planned news conference with Luxembourg's Prime Minister Xavier Bettel.
The pair were due to hold a joint news conference however Mr Johnson did not take part in the media briefing.
According to a UK source, the prime minister was due to tell Mr Juncker that he wanted a deal on the Withdrawal Agreement but that it could not include the backstop guaranteeing no hard border in Ireland.
Officials in Brussels cautioned that today's meeting was the only opportunity for the two men to meet this side of a crucial EU summit in the middle of October.
Mr Johnson was accompanied by British Brexit Secretary Steve Barclay who was due to hold separate talks with the EU's chief Brexit negotiator Michel Barnier.
UK sources say the meeting will build on what they describe as the extensive engagement made by Mr Johnson's chief negotiator David Frost during meetings in Brussels which they say have made positive progress.
However, EU sources say the meeting last Friday was the first time the British side had shown positive engagement.
London appears to be willing to concede an all-Ireland agri-food regime, aligned with EU regulations, as the first step towards replacing the backstop.
However, Dublin and Brussels have signalled that this will not go nearly far enough if a hard border is to be avoided, the all-island economy protected, and North-South cooperation preserved.
Much attention is on the DUP and how far it will be prepared to go to soften its hard opposition to the backstop.
A UK source had said Mr Johnson will make it clear to President Juncker that he will reject another extension to the Article 50 negotiations, if offered.
Additional reporting: Reuters, Tony Connelly