European Commission President Jean-Claude Juncker (right) shakes hands with British Prime Minister Boris Johnson prior to a meeting at a restaurant in Luxembourg on Monday. Johnson was holding his first meeting with Juncker in search of a long-shot Brexit deal. Photo: AP

The European Union's two top officials handling troublesome Brexit negotiations warned Wednesday that the risk of a no-deal exit looms large unless Prime Minister Boris Johnson's government offers concrete proposals.

"The risk of a no deal remains very real. That will maybe be the choice of the United Kingdom but never the choice of the European Union," European Commission chief Jean-Claude Juncker told the European Parliament in Strasbourg.

The warning came two days after Juncker and British Prime Minister Boris Johnson met in Luxembourg for talks, just six weeks before Britain is set to exit the bloc.

That trip ended in humiliation for Johnson after he avoided what was meant to be a joint press conference with his Luxembourg counterpart, put-off by a small anti-Brexit protest nearby.

Juncker emphasized the UK still has not offered any viable solutions to rewrite a withdrawal agreement struck by Johnson's predecessor but rejected three times by the British parliament.

Juncker said "I am not sure" that a new deal would be reached. 

"We have very little time left. But I am sure we must try," said the EU leader, whose mandate ends on October 31 - the deadline for Britain to leave the EU.

The strident message parallelled stepped-up moves by Brussels and London to hand out blame for a chaotic no-deal Brexit.

The EU's pointman in the negotiations, Michel Barnier, told MEPs in Strasbourg that "it is certainly not a question of pretending to negotiate."

He added that "it is our responsibility to pursue this process with determination, with sincerity."

His words were taken as a dig at Johnson, who is seen by many in Brussels and London as running down the clock to have Britain exit the EU "with or without" a new deal.