"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 do what they did for months - run down the clock.
The European Parliament's Brexit co-ordinator Guy Verhofstadt said the extension risked importing the "Brexit mess into the EU" and "poisoning" the European Parliament elections. "However, this is not an excuse to say, 'let's get it over with, ' just because we're exhausted".
Writing in the Observer on Sunday, Mr Blair and Mr Ahern said, "Following the Good Friday agreement, there were two referendums".
And moreover that it will poison the upcoming...
"We should approach this seriously, as UK Members of the European Parliament will be there for several months, maybe longer". I also can not agreed to accept a second category of membership.
"Therefore I also ask you to reject similar ideas if they were to be voiced in this House".
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".
Other EU leaders in the room remembered that fact and reminded Tusk that it is not their decision to make.
"Meanwhile, US Speaker of the House of Representatives Nancy Pelosi has said there would be no chance whatsoever" of a post-Brexit trade deal between the US and United Kingdom if there was any weakening of the Good Friday Agreement. I didn't respond at the time, but today, in front of you, I would like to say: "at this rather hard moment in our history, we need dreamers and dreams", he added.
"We can not give in to fatalism".
"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".
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.
He said that with the UK holding European Union elections in May, unless Mrs May's deal is ratified by MPs before then, he fears the arrival of a new transient set of UK MEPs.