The UK has yet to come forward with a solution to replace the backstop, the European Commission says.
Downing Street said a meeting between Boris Johnson and Commission president Jean-Claude Juncker was “constructive”.
In a statement after the working lunch, the Commission said no proposals had been put forward to replace the controversial Brexit policy.
Mr Johnson has called the backstop “undemocratic” and said it needed to be removed from any deal with the EU.
A Downing Street spokesperson said Mr Johnson also reiterated he would not request an extension and would take the UK out of the EU on 31 October.
The EU has said it is willing to look at alternatives, but that an insurance policy like the backstop must be in place.
The backstop is the controversial policy in the existing withdrawal agreement, rejected three times by MPs, which would require the UK to follow the EU’s customs rules to ensure there are no physical checks on the border between Northern Ireland and the Republic.
The prime minister had been due to speak at a press conference after meeting Mr Juncker and Luxembourg Prime Minister Xavier Bettel.
However, his appearance was cancelled after a group of anti-Brexit protesters heckled Mr Johnson near to the courtyard where it was due to be held.
Instead, Mr Bettel took questions alone from the press, saying the “only solution” was the existing withdrawal agreement.
He said there were “no concrete proposals at the moment on the table” from the UK and said the EU “needs more than just words”.
“We need written proposals and the time is ticking so stop speaking and act,” he said.
“But we won’t accept any agreement that goes against a single market, who will be against the Good Friday Agreement.”
Mr Johnson said the EU must make “movement” in its opposition to scrap the Irish backstop, but insisted there was “just the right amount of time” to get a deal done.
When asked what concrete proposals he had made, Mr Johnson said “there’s been a lot of work” and “papers have been shared”.
“We’ve got to manage this carefully. Yes, we’ve got a good chance of a deal. Yes, I can see the shape of it. Everybody could see roughly what could be done,” he said.
He reiterated that the UK will come out of the EU on 31 October “deal or no deal”.