Speaking on the same occasion, the head of the bloc's executive European Commission, Jean-Claude Juncker, also reminded London there was no time to waste before Britain leaves the bloc, as is due in March 2019.
The EU parliament approved a text that says Britain should, among other things, not be able to cherry-pick benefits of the EU market in any agreement on future relations, AP reports.
The EU and Britain are hoping to seal a deal this month on a transition period after Brexit, and start talks on their future relationship this spring.
Mr Juncker today said the draft proposals should not come as a surprise or shock, suggesting it "translates faithfully" the agreement reached between British and European officials late a year ago to avoid a hard border.
During his speech, Juncker said the issue of Ireland was a European one, but was interrupted by members of the parliament saying this was only a British issue.
Jens Stoltenberg, secretary-general of the US-led North Atlantic Treaty Organisation alliance, said the attack was "horrendous".
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The European Parliament - which will have the final veto on any Brexit deal - will vote on Wednesday on a proposal to offer Britain an "association agreement" which it says would be broader than a trade deal.
Other sticking points will be avoiding a hard border in Ireland, as well as securing citizens' rights.
It's "rather surprising" that May thinks the European Union would accept "convergence as sought by the United Kingdom and at the same time open up the possibility of divergence" when it gives Britain a comparative advantage, Barnier said.
BDI chief Lang said: "The minimum requirement for German companies is trade in goods without customs duties or quotas, ideally in a customs union". "That can not happen", the European Parliament's Brexit negotiator Guy Verhofstadt told Euronews.
And as for May's plan for the U.K.to get observer status in some key EU industry regulators: "You can't want to participate in our agencies without a legal commitment of applying the rules of the Union and jurisdiction of the Court of Justice". In his words, it is now time to turn "speeches into contracts, engagements into agreements and move from speeches, common assumptions and desires for future relationships to concrete, applicable solutions".
UKIP MEP and former party leader Nigel Farage finds that outrageous. If we go for transition, we stay inside a Customs Union.