European Council president Donald Tusk insisted that if British MEPs are elected in May they must be treated as "full members", as he hinted that the UK could delay Brexit beyond October.
Addressing the European Parliament in Strasbourg, Tusk said: "One of the consequences of our decision is that the UK will hold European elections next month.
"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 the 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."
Tusk also said the European Union did not give into "fear and scaremongering" about the UK disrupting the EU's functioning during a Brexit 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."
European Commission president Jean-Claude Juncker said the EU is "ready" for a no-deal Brexit but that the EU has "nothing to gain" from the "disruption" it would cause the UK.
He 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 said he fears Brexit will "poison" the European elections.
Referring to the delay to Brexit, 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 has claimed his party would win a general election if Theresa May and Jeremy Corbyn agree to a permanent customs union compromise.
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 May and the opposition of 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."
Asked what progress there had been in Brexit talks with the Government, Jeremy Corbyn said Labour had put its case that the future relationship with Europe had to be one where there was a customs union.
He said: "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."
He added: "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.
"I don't want to do that."
Corbyn said the talks were continuing. He added: "We've lost a lot of time by the dithering of the Government on bringing issues to Parliament."
Corbyn said: "Nigel Farage is not the answer to anyone's problem.
"We have to have a relationship with Europe in or out of the EU. We have a major trading partnership with Europe and all Farage is offering is some kind of never-never-land, saying we'll walk away from everything.
"Well, he should say that to those people whose jobs would be at risk in manufacturing industries and food processing industries. He should say that to those people who are really going to suffer as a result of this.
"We're serious about having a trading relationship with Europe. We're serious about our relationship with the rest of the world. I'm not sure he is."
Asked whether the Brexit Party was a risk to Labour and Conservative in the European elections, he said: "We will fight the elections as a party that is committed to that relationship with Europe but above all it's about uniting people however they voted in 2016, they're suffering from austerity."
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