European Council president Donald Tusk said he still believed that Brexit could be reversed after the UK’s departure from the EU was delayed until October 31.
Mr Tusk told MEPs that the UK would continue to be represented in the European Parliament for “several months – maybe longer”.
The prospect of the UK taking part in the May 23 elections, almost three years after voting to leave the European Union, has fuelled anger among Brexiteers.
Theresa May secured the extension to the Brexit process at a summit last week in order to prevent a no-deal split from the EU, but still hopes the UK can leave earlier than the Halloween deadline if she can get a Withdrawal Agreement through the Westminster Parliament.
Cross-party talks with Labour aimed at securing a Commons majority for a deal are continuing but Jeremy Corbyn said “there’s no agreement yet” and “the Government doesn’t appear to be shifting the red lines”.
Speaking in Strasbourg, Mr Tusk said he disagreed with one of the bloc’s premiers who had said the EU should abandon hope of the UK reversing its decision to leave.
“During the European Council one of the leaders warned us not to be dreamers, and that we shouldn’t think that Brexit could be reversed,” he said.
“I would like to say: at this rather difficult moment in our history, we need dreamers and dreams.
“We cannot give in to fatalism. At least I will not stop dreaming about a better and united Europe.”
European Commission president Jean-Claude Juncker told MEPs the EU has “nothing to gain” from the disruption a no-deal Brexit would bring to the UK.
Mr Juncker said: “We have adopted the necessary contingency measures and we are ready for a no-deal Brexit.
“But our union has nothing to gain from great disruption in the United Kingdom. The only ones who would benefit are those who resent multilateralism and seek to undermine the global legal order.”
European Parliament chief Brexit co-ordinator Guy Verhofstadt expressed his fear that Brexit will “poison” the European elections.
Referring to the delay to Brexit, he said: “I fear that it will continue the uncertainty. I fear that it will prolong the indecision. And I fear most of all that it will import the Brexit mess into the European Union.
“And moreover, that it will poison the upcoming European election.”
Brexit Party leader Nigel Farage claimed his party would “sweep the board” at the elections on May 23 – and would win a general election if Mrs May and Mr Corbyn agree to the “betrayal” of a permanent customs union.
He told the European Parliament: “The Brexit Party will sweep the board in these elections and there is only one way it can be stopped and that is if the governing party of Mrs May and the opposition of Mr Corbyn come together and agree to a permanent customs union, and indeed effectively membership of the single market.
“If that happens, the Brexit Party won’t win the European elections but it will win the general election because the betrayal will be so complete and utter, so I don’t believe it’s going to happen.”
In Westminster, cross-party talks between Labour and the Government were expected at an official level.
Mr Corbyn said Labour had put its case that the future relationship with Europe had to mean a customs union.
He added: “There has to be access to European markets and above all there has to be a dynamic relationship to protect the conditions and rights that we’ve got for environment and consumer workplace rights.
“We’ve put those cases very robustly to the Government and there’s no agreement as yet, we’ve put the case, we’ve had quite interesting, quite long technical discussions particularly on environment regulations.”
But he said Mrs May was under pressure from Tories who wanted a trade deal with US President Donald Trump.
“The Government doesn’t appear to be shifting the red lines because they’ve got a big pressure in the Tory party that actually wants to turn this country into a deregulated low tax society which will do a deal with Trump,” he said.
“I don’t want to do that.”
Meanwhile, the pro-EU Independent Group set up by MPs who defected from Labour and the Conservatives has officially become a registered political party called Change UK.
This means they can field candidates at the May 23 European elections.