Mr Verhofstadt said delaying Brexit to the end of October risked prolonging the uncertainty of the process because it was "too near for a substantial rethink and at the same time too far away to prompt any action".
European Council President Donald Tusk said on Tuesday that no one should give up on the "dream" that the United Kingdom might reverse course on Brexit, and urged EU politicians not to push for a quick exit out of mere exhaustion.
Senior MEP Guy Verhofstadt said to Mr Tusk that "Instead of sending May back to London with no extension or ultimately a very short one - a few days, a week - you gave her six months".
He told the European Parliament: "The proof of this was that the first thing that after last week's decision was to go on holidays".
"We have adopted the necessary contingency measures and we are ready for a no-deal Brexit", he told MEPs.
"And moreover that it will poison the upcoming European election".
But today in front of you I would like to say at this rather hard moment in our history, that we need the dreamers and dreams.
He said they will have "all the rights and obligations" of full members.
Meanwhile, Foreign Secretary Jeremy Hunt Jeremy Hunt has said continuing Brexit "paralysis" will be "highly damaging" to the UK.
The European Parliament's Brexit coordinator Guy Verhofstadt unexpectedly said Nigel Farage's Brexit Party could "save the EU" by forcing Labour and the Conservatives to reach a compromise and avoid the EU "importing the Brexit mess" in European elections. "You can not drag out Brexit for a decade".
"We can not give into fatalism", Tusk said in a report to the European Parliament.
"My message is that, whatever the outcome of Brexit, Britain is going to be the best place in Europe to invest in with our top universities, the best universities in Europe, with more tech start-ups than France, Germany, and Italy combined".
Nigel Farage claimed his new Brexit Party would "sweep the board" at the elections on May 23.
European Council President Donald Tusk admitted on Tuesday that not only is he opposed to the UK's decision to leave the EU, but it's his goal to "reverse Brexit".
Parliament is now in recess for Easter, but cross-party talks between the government and Labour are expected to continue today at an official level.