Tajani told reporters in London after meeting with May that a new UK government would be a positive move, especially before official Brexit negotiations get underway.
"I think is good not only for the UK, but also for us because we will have the same prime minister, the same ministers, the same negotiator for the next years."
Britain voted to leave the EU last June and May formally triggered Article 50, the EU's divorce clause, on March 29, beginning what are set to be at least two years of difficult negotiations before Britain finally leaves.
Tajani said he wanted a "framework" deal on Britain's exit from the EU to be settled before the end of 2017, allowing negotiations to begin on the future relationship "immediately thereafter."
"And we [will] know the real situation in the UK, we [will] know the government. … It's better for us to work with the same government and not with a potential election campaign," he added.
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 hard-line Brexit settlement in order to assuage core Conservative voters and her 50 or so more hard-line Brexit-supporting MPs.
Citizens' rights a priority
Tajani also stressed that an early agreement on the rights of EU citizens living in the UK was a European Parliament priority.
A British government spokesman said the two politicians had agreed on the importance of legal security for UK citizens in the EU and EU citizens in the UK.
In early April, the EU Parliament agreed on a tough negotiating line with London, saying there would be no financial concessions or cherry-picking.
The European Parliament is not directly involved in the forthcoming talks on Brexit but is regularly informed and has to agree to a future agreement between the EU and the UK.
EU Commission-UK talks next week
EU Commission head Jean-Claude Juncker and the bloc's chief Brexit negotiator, Michel Barnier, will hold talks with May in London next Wednesday, commission spokeswoman Mina Andreeva told reporters Thursday.
"President Juncker will travel to London at the invitation of Prime Minister May to discuss the process of the Article 50 negotiations between the EU 27 represented by the commission and the United Kingdom," Andreeva added.
Barnier and Juncker's chief of staff Martin Selmayr will accompany Juncker for the talks at Downing Street.
The announcement of the visit comes just two days after May announced plans to hold a snap general election in Britain on June 8 in what she hopes will give her a "mandate to complete Brexit."
EU leaders will meet in Brussels on April 29 to formally approve guidelines for the negotiations.
Barnier is expected to get a formal mandate to begin talks on May 22 although they are not now expected to begin in earnest until after the British election.
jbh/rc (AFP, dpa)