European Council president Donald Tusk has urged the European Parliament to "be open to a long extension, if the UK wishes to rethink its strategy".
He said: "You cannot betray the six million people who signed the petition to revoke Article 50, the one million people who marched for a People's Vote, or the increasing majority of people who want to remain in the European Union."
In a tweet, released after his speech, he added that the parliament should be open to a long extension.
Appeal to EP: You should be open to a long extension, if the UK wishes to rethink its strategy. 6 million people signed the petition, 1 million marched. They may not feel sufficiently represented by UK Parliament but they must feel represented by you. Because they are Europeans.— Donald Tusk (@eucopresident) March 27, 2019
Speaking at the European Parliament in Strasbourg, Mr Tusk described opposition to a long extension on grounds that it "did not suit" some EU members as "unacceptable".
Speaking in the same session, European Commission President Jean-Claude Juncker said a sphinx was an "open book" by comparison to the UK, in terms of clarity on Brexit.
"If I were to compare Great Britain to a sphinx, the sphinx would be an open book by comparison.
"And let's see how that book speaks over the next week, or so," he said.
European Parliament Brexit co-ordinator Guy Verhofstadt attacked claims that the EU had tried to humiliate and punish the UK.
He told the European Parliament: "You know what the problem is? The problem of the humiliation and punishment is because of the mess in the Tory Party - there is the humiliation of the British people."
I’m surprised to see you here, Mr. Farage. I thought you were marching 200 miles for the leave campaign? How many did you do? 2 miles! You remind me more & more of Field Marshal Haig in Blackadder, sitting safely in his office, while his people are walking in the cold & the rain.— Guy Verhofstadt (@guyverhofstadt) March 27, 2019
The EU’s Chief Brexit negotiator, Michel Barnier, addressed Brexit Party MEP Nigel Farage on the floor of the European Parliament.
Mr Barnier told Mr Farage the EU respected "the sovereign decision of the majority" in the 2016 referendum on EU membership and said "no one is trying to steal Brexit".
Mr Barnier said that the EU had been seeking specific solutions for two years on Brexit.
He also told the parliament that the Good Friday Agreement would continue to apply, regardless of the manner in which the UK leaves the EU.
He said that additional resources and technical help would be provided to Ireland for disruption caused by Brexit.
"In all scenarios, the Good Friday agreement will continue to apply. The United Kingdom will remain a core guarantor of that agreement and is expected to uphold it in spirit and in letter," he said.
"The commission is ready to make additional resources available to Ireland, technical and financial to address any additional challenges," he continued.
Mr Farage told the parliament that it was "inevitable" that the UK was heading for a delay.
"You should ask yourselves: 'Do you really want that?"' he told MEPs. "Do you really want Brexit to utterly dominate the next couple of years of your business to the exclusion of your many other ambitions?
"Do you really want the UK to contest the European elections, to send back a very large number of Leave MEPs, just at a time when you are fighting populism - as you see it - across the continent?"
And, to cries of "No" from some MEPs and "Yes" from others, he asked: "Do you really want me back in this place?"
Meanwhile, the DUP's only member of the parliament said the party will not accept Mrs May's Brexit deal as it would endanger the integrity of the UK.
"The DUP wants to leave the European Union in an orderly fashion but this deal will endanger the constitutional and economic integrity of the UK," a party statement quoted Diane Dodds as telling the parliament.
"It is not a price that we as Unionists are willing to pay," she added.
Additional Reporting PA