His appeal comes after he met UK Prime Minister Boris Johnson for a working lunch in Luxembourg on Monday.
Johnson, however, again insisted he will not ask for an extension to Article 50 and still planned to see the UK leave the EU on 31 October with or without a deal.
Last week UK MPs passed a law that will require Boris Johnson to ask the EU to extend the 31 October deadline if a deal was not agreed by 19 October, two days after an EU summit in Brussels.
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Johnson told the Mail on Sunday newspaper in the UK that, on that date, the UK would break out of its "manacles" like cartoon character The Incredible Hulk - with or without a deal.
The aim of Monday’s meeting, said Juncker, was to take stock of the ongoing technical talks between the EU and the UK and to discuss the next steps.
However, with the clock ticking on the Halloween deadline for the UK’s EU exit, the get together appears to have left the two sides as far apart as ever.
Afterwards, Juncker said “it is the UK's responsibility to come forward with legally operational solutions that are compatible with the Withdrawal Agreement.”
“It is the UK's responsibility to come forward with legally operational solutions that are compatible with the Withdrawal Agreement" Jean-Claude Juncker
Juncker underlined the Commission's “continued willingness and openness to examine whether such proposals meet the objectives of the backstop.”
Pointedly, he said, “Such proposals have not yet been made.”
The Commission, he said, “will remain available to work 24/7” and the October European Council will be an “important milestone in the process.”
“The EU27 remain united,” he said in a statement.
Juncker was accompanied by the Commission's chief Brexit negotiator, Michel Barnier.
Juncker, due to leave office in the next few weeks, will travel to Strasbourg later on Monday and address the plenary session of the European Parliament on Wednesday morning.
The UK, in contrast to Juncker’s downbeat account, has described the meeting as “constructive.”
"The Prime Minister also reiterated that he would not request an extension and would take the UK out of the EU on the 31st October" Downing Street spokesperson
On Monday, a Downing Street spokesperson, in a statement, said: “The Prime Minister and President Juncker had a constructive meeting this lunchtime. The Brexit Secretary and Michel Barnier were also in attendance.”
“The leaders took stock of the ongoing talks between the UK’s team and Taskforce 50. The Prime Minister reconfirmed his commitment to the Good Friday/Belfast Agreement and his determination to reach a deal with the backstop removed, that UK parliamentarians could support.”
“The Prime Minister also reiterated that he would not request an extension and would take the UK out of the EU on the 31st October.”
“The leaders agreed that the discussions needed to intensify and that meetings would soon take place on a daily basis. It was agreed that talks should also take place at a political level between Michel Barnier and the Brexit Secretary, and conversations would also continue between President Juncker and the Prime Minister.”
Meanwhile, the European Parliament is set to debate Brexit in Strasbourg this week.
Ahead of the debate, Pedro Silva Pereira, a Vice-President of the European Parliament and S&D interim member of the Brexit Steering Group, told this website this comes amid “worrying signals being sent by Boris Johnson and his government on a damaging no-deal outcome.”
“Even if we regret Brexit, our group has worked in a responsible way to mitigate its worst consequences and ensure that the UK leaves the EU in an orderly way. Our priorities remain ensuring that the rights of EU citizens are guaranteed in all circumstances and protecting the peace process in Northern Ireland.”
“We are also deeply concerned by the difficulty EU citizens, some of whom have lived in the UK for decades, have had in receiving settled status from UK authorities.”
“This combined with confusing and contradictory statements from the UK Home Office on ending freedom of movement after October 31 are causing stress and uncertainty for millions of people who have chosen to build their lives in the UK.”
“People should not pay the price, so our Group supports ring-fencing citizens’ rights whatever happens. We support an extension of Article 50, if needed, to avoid a catastrophic no deal scenario.”
Further comment came from EPP leader Manfred Weber, who said, “The EPP’s principles are clear: we will protect our interests, our citizens and our values. While we are getting ready for the worst-case scenario of a no-deal Brexit, we remain ready and united to find solutions together with the UK.”