Guy Verhofstadt says the delay is "too near for a substantial rethink of Brexit" and "too far away to prompt any action".
A top EU figure has said he fears Britain will waste its latest Brexit reprieve and "run down the clock" once again.
European Parliament Brexit co-ordinator Guy Verhofstadt told the European Parliament that the bloc's decision to grant a delay until the end of October risked prolonging the uncertainty.
He said the six-month extension to Article 50 is "too near for a substantial rethink of Brexit and at the same time too far away to prompt any action".
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"My fear is that with this decision, the pressure to come to a cross-party agreement disappears," Mr Verhofstadt said, referring to the talks between Labour and the Conservatives to try and find a Brexit compromise.
"And that both parties, the Conservatives and Labour, will again already what they did for months - run down the clock.
"And the proof of this is that the first decision the House of Commons took after your decision was to go on holidays."
Mr Verhofstadt said the prospect of both parties being "wiped out" in May's European Parliament elections at the hands of Nigel Farage's Brexit Party could be an unlikely solution.
"So really, I never thought I'd say this in my life here in this parliament, but maybe the only thing that can save us is Nigel Farage now," he said to applause in the chamber.
Mr Verhofstadt said his advice to both parties would be to come to an agreement to "in the coming days to avoid this imminent disaster".
Mr Farage predicted his party would "sweep the board" in the elections.
He added: "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."
Meanwhile, European Council President Donald Tusk said the UK cannot be treated as a "second category" member of the EU if it ends up taking part in the elections.
"One of the consequences of our decision is that the UK will hold European elections next month," he told the gathering in Strasbourg.
"We should approach this seriously, as UK Members of the European Parliament will be there for several months, maybe longer.
"They will be full Members of the Parliament, with all their rights and obligations.
"I am speaking about this today because I have strongly opposed the idea that during this further extension, the UK should be treated as a second-category member state.
"No, it cannot. Therefore, I also ask you to reject similar ideas, if they were to be voiced in this House."
Mr Tusk said that the EU did not give into "fear and scaremongering" about the potential for the UK to be a disruptive force in the bloc during an extension.
He said: "I know that some have expressed fear that the UK might want to disrupt the EU's functioning during this time but the EU 27 didn't give in to such fear and scaremongering.
"In fact, since the very beginning of the Brexit process the UK has been a constructive and responsible EU member state and so we have no reason to believe that this should change."
Mr Tusk also said he still believed Brexit could be reversed, adding that he disagreed with one of the bloc's premiers who had said the EU should abandon hope of the UK changing its mind.
"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 also addressed MEPs, telling them that the EU is "ready" for the possibility of Britain leaving at the end of October with no deal.
But he said Brussels has "nothing to gain" from the "disruption" it would cause the UK.
Parliament is currently in recess for Easter, but cross-party talks between the government and Labour are expected to continue today at an official level.
Jeremy Corbyn said "there's no agreement yet" and the government "doesn't appear to be shifting the red lines".
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