European politicians had expressed fears that concluding negotiations so close to a national vote in 2020 - when the next general election would have been held if not this June - could have forced May to seek a more hardline Brexit settlement in order to assuage core Conservative voters and her 50 or so more hardline Brexit-supporting MPs.
Mr Tajani, whose organisation has a veto on the final Brexit withdrawal deal, said the meeting went well.
The meeting will be used to agree the guidelines for the European Union negotiating team headed by Michel Barnier.
The tough negotiating guidelines set out tight protections for EU citizens and budgets, as well as European businesses whose goods are traded in the UK.
It would be modelled after the Youth Mobility Scheme, which now allows 18- to 30-year-olds from non-EU countries such as Australia, Canada and New Zealand to work in the United Kingdom for up to two years.
The EU has already voiced concern that British red tape is making it hard to claim rights to permanent residence after five years and the paper said it must have a "simple and swift" procedure in place that should be free or at worst no more expensive than Britons paid for similar public documents. I am very clear that we want migration at sustainable levels.
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Prime Minister Theresa May formally began Britain's break up from the European Union in March, declaring there was no turning back, ushering in a tortuous exit process that would test the bloc's cohesion and pitch her country into the unknown.
The EU parliament president nonetheless welcomed May's decision to call a snap election, saying it was unlikely to delay Brexit talks by more than a week and would provide long-term clarity.
"Under the (Brexit) treaty everything under the treaty is under the court", Mr Tajani said.
"Instead (she will) be open to the sort of arrangements with the European Union that hardliners in her Conservative Party have been condemning as a "soft Brexit", Merritt said in a commentary.
"It is better for us to work with the same government and not with a potential election campaign [looming]". Its executive director, Adam Farkas, said last month that Brexit was a "major talking point among the staff" at its Canary Wharf headquarters.
The memo also says the European Commission and its agencies are expected to "take account" of the fact that Britain will be "a third country" in two years, when concluding multibillion-euro contracts and appointing staff.
"I will inform the [European] council of this meeting and that it was positive".