It is up to the UK if talks to end EU membership result in a "good deal, no deal or no Brexit", Donald Tusk said on Tuesday, reviving the possibility Britain may not leave the bloc after all.

Senior EU leaders addressed legislators at the European Parliament in Strasbourg who were debating last week's EU summit, during which leaders declared "insufficient progress" had been made in Brexit talks to immediately advance to trade discussions.

There are three "separation" challenges that need to be negotiated: the UK has to "settle its accounts" before exiting, statues of EU citizens in the UK and Britons in the EU must be determined, and a decision must be made regarding what happens with the Northern Ireland border once the UK exits the EU.

Despite the challenges ahead, European Council President Tusk emphasized the importance of unity, describing the UK's planned departure as the EU's "toughest stress test".

"We have managed to build and maintain unity among the 27. But ahead of us is still the toughest stress test. If we fail it, the negotiations will end in our defeat," Tusk said.

"It is, in fact, up to London how this will end: with a good deal, no deal or no Brexit. But in each of these scenarios, we will protect our common interest only by being together," he added.

The European Council president also said there would be a special EU summit in February next year to decide how the composition of the European Parliament should be changed after Brexit.

European Commission President Jean-Claude Juncker insisted the European Commission is "not negotiating in a hostile mood".

"We want a deal. Those who do not want a deal - the no-dealers - they have no friends in the Commission," he said, continuing: "We want a fair deal with Britain and we will have a fair deal with Britain. The no-deal is not our working assumption."

British Prime Minister Theresa May told British lawmakers on Monday she is "positive and optimistic" about moving on in Brexit negotiations.

British voters opted to leave the EU in a referendum over a year ago and Brexit negotiations are expected to be finalized in March 2019.