In a non-binding resolution passed on Wednesday morning, the European parliament voted 544 in favour of another potential extension beyond October 31, with 126 against and 38 abstentions.
During a three-hour debate, the session in Strasbourg heard EU Brexit chief negotiator Michel Barnier say he wants to keep working "night and day" in order to find a satisfying Brexit deal for both parties.
He urged Prime Minister Boris Johnson and his team to make concrete proposals.
His language may signal a change in tack from the EU side on Brexit, as he sought to reassure MEPs that the Commission is "prepared to work day in day out, morning until night" to try and reach a deal.
But he added: "I am not sure that we will get there."
Meanwhile, Brexit Party leader Nigel Farage labelled Luxembourg's leader as a "pipsqueek prime minister" after Xavier Bettel set out to "ritually humiliate" Mr Johnson when the pair met on Monday.
He was refering to what should have been a joint press conference between Mr Johnson and Mr Bettel, which was disrupted due to noisy pro-EU protesters.
Mr Johnson's team had asked for the press conference to be moved indoors to avoid hecklers, but Luxembourg rejected the idea, leaving Mr Bettel to speak alone and attack the British PM for the Brexit "nightmare".
Mr Farage said a Brexit deal relies on "good faith" from the EU but suggested "events that we've seen across Europe this week do not indicate that good faith".
But in any case, according to Prime Minister Johnson, essential for a deal is the removal of the Northern Ireland backstop from the Withdrawal Agreement.
Mr Juncker explained how chief negotiator Michel Barnier is still waiting for written proposals from Prime Minister Johnson on how to solve the issue of the backstop.
"The position of the European Union has never been an ideological one" he said of the backstop.
"It has always been a pragmatic one."
"The new UK Government this week in Luxembourg outlined the aspects of the backstop they don't like. That is not enough, however, to move towards achieving a solution."
He added: "There is very little time remaining but what I do know is that we have to keep trying."
He told MEPs in Strasbourg, France, that a no-deal Brexit "might be the choice of the UK, but it will never be ours."
For Mr Johnson and many others in the UK, the main sticking point over a Brexit deal is the Irish border backstop.
It is a safety net which would require Britain to retain some EU trade rules in order to avoid a hard border between EU member Ireland and Northern Ireland.
Critics of the backstop say it is undemocratic and would lock the UK into a relationship with the EU that it may not be able to leave.
"I asked the British prime minister to specify the alternative arrangements that he could envisage," Juncker said.
"As long as such proposals are not made, I cannot tell you while looking you straight in the eye that progress is being made."
Mr Farage said it was clear from the "emollient" comments by Mr Juncker that they were "very close" to a deal at the EU summit next month in Brussels.
Spelling out the need for the backstop, Mr Barnier, speaking after Mr Juncker, warned that even if Britain leaves with no agreement, major problems will still have to be resolved.
Issues he said include the future of EU citizens in the UK, peace in Northern Ireland and the protection of the EU's single market and the Irish economy.
"None of these questions disappears," Barnier said, insisting that the challenges must not be underestimated.
"We need legally operative solutions in the withdrawal agreement to respond precisely to each problem to address each risk that Brexit creates."
"Some three years after the British referendum, it's not a question of pretending to negotiate. It's our responsibility to continue this process with determination and sincerity," Barnier told MEPs.
The debate in Strasbourg came as Jeremy Corbyn set out his approach to Brexit, with a hint that he would remain neutral in any referendum called by a Labour government.
Writing in The Guardian, Mr Corbyn said: "A Labour government would secure a sensible deal based on the terms we have long advocated, including a new customs union with the EU; a close single market relationship; and guarantees of workers' rights and environmental protections.
"We would then put that to a public vote against Remain, and I pledge to carry out whatever the people decide, as a Labour prime minister."We are the only UK-wide party ready to put our trust in the people of Britain to make the decision."