In their speeches, both Davis and Barnier referred to British Prime Minister Theresa May's speech in Florence last month, which they believed brought a new dynamic to the talks in Brussels.

"The Prime Minister's speech set out the scale of our ambition for our deep and special partnership with the European Union ... I hope the leaders of the 27 will provide Michel with the means to explore ways forward with us on that and to build on the spirit of cooperation we now have," said Davis.

For Barnier's part, May's speech strengthened his belief that "with political will, decisive progress is within our reach in the coming weeks," he said, asserting that "the agreement that we are working towards will not be built on 'concessions'... but shared objectives, obligations, duties and solutions."

But Barnier's remarks about concessions appeared to be nothing but a paronomasia, as it was the absence of concessions that made him "not able to recommend to the European Council next week to open discussions on the future relationship."

In the middle of the fifth round talks, President of the European Council Donald Tusk said on his twitter account Tuesday that EU27 are not working on a "no deal" scenario in their Brexit talks with Britain.

"We negotiate in good faith and hope for 'sufficient progress' by December," he said.

Tusk's remarks came a day after May told Britain to prepare for a no-deal Brexit.

Addressing MPs in the House of Commons on the first day back after the conference season, May said achieving a special partnership after Brexit will require leadership and flexibility, not just from Britain, but from the 27 nations of the EU.

"As we look forward to the next stage, the ball is in their court. But I am optimistic it will receive a positive response," May told MPs in her first parliamentary statement since her big speech in Florence.

"What we are seeking is not just the best possible deal for us, but I believe that will also be the best possible deal for our European friends too. Progress will not always be smooth but by approaching these negotiations in a constructive way in a spirit of friendship and cooperation and with our sights firmly set on the future, I believe we can prove the doomsayers wrong," May added.

In her statement, May said the British government had on Monday published two new policy consultation statements on trade and customs.

"These pave the way for legislation to allow the UK to operate as an independent trading nation and to create an innovative customs system that will help us achieve the greatest possible tariff and barrier-free trade as we leave the EU," said May.

Also on Monday, the fifth round of Brexit negotiation started in Brussels. With the absence of Britain's Davis, the two sides kicked off their talks in a low profile -- no joint press conference.

Prior to her speech in the House of Commons, May told the other 27 members of the Union that "the ball is in the EU's court," calling on EU to take actions and exert more flexibility and imagination in the negotiations.

Answering the question of a British reporter about "the ball is in whose court," Margaritis Schinas, European Commission (EC) chief spokesperson, told reporters during Monday's daily briefing in the headquarters of the EC that "This is not exactly a ball game."

"You know we don't provide comments on comment, but what I can remind you is that there is sequencing of these talks," he said.

"There is no solution found so far to the step one, that is the divorce proceedings, so the ball is entirely in the UK's court for the rest to happen," said Schinas.

The long-awaited Brexit talks was launched on June 19, nearly one year after Britain voted to leave the bloc by a narrow margin on June 23, 2016.

May sent a notification letter to the EU in late March, triggering a two-year countdown to Britain's withdrawal of the bloc after more than 44 years of membership.