"I wish also to be understood by the people who speak French, especially two days before the crucial election in my country, but it is equally important for me to be understood by the British people", Barnier said.
The EU's chief Brexit negotiator, Michel Barnier, says the United Kingdom must agree to "crystal-clear guarantees" to protect the rights of EU citizens.
"There should be no doubt that the European Union is not abandoning the United Kingdom; it is the opposite, they are abandoning the European Union and this is a difference that will be felt over the next few years", he told his audience.
Brussels was quick to dismiss the claims, with European Union president Donald Tusk on Thursday cautioning against letting "emotions get out of hand" before formal negotiations are due to begin after Britain's June vote.
Mrs May was put on the defensive this week after leaks about a disastrous dinner in London with European Commission president Jean-Claude Juncker and Mr Barnier.
On Wednesday, a senior European Union source told the BBC the PM's suggestion that officials were trying to affect the election result was "pure fantasy".
We must keep in mind that in order to succeed, today we need discretion, moderation, mutual respect and a maximum of good will'.
Antonio Tajani's denial came after a spokesman for European Commission president Jean-Claude Juncker dismissed the allegation by saying his office was "too busy" to meddle in the election.
Juncker, who said the comment with a smile, described Brexit as "a tragedy".
"Our British friends have chose to leave, which is a tragedy", the former Luxembourg Prime Minister told the European University Institute's State of the Union conference.
He supported May's belligerent rhetoric too, saying the PM "was right to point out to everybody that these negotiations are going to be not just hard, but extremely tough, and to rightly point out how they are going to be dealt with".
Juncker's executive Commission, meanwhile, is said to be too busy to interfere in the British elections.
She said these were "deliberately timed to affect the result of the general election that will take place on June 8". People get excited whenever we have elections.
Barnier told reporters that Britain's relations with its 27 European partners once it leaves will center "around a free trade agreement, but it's not the moment to talk about it immediately".
"The European Commission has tightened its negotiating position".
Roger Scully, a politics professor at the University of Cardiff in Wales, said the national picture would inevitably have some effect on the vote: "The Conservatives are doing very well and this is nearly certainly likely to have some spill-over into the local elections".
Acting on past year s referendum, May gave the European Union formal notice of Britain s intention to leave the bloc on March 29, and two weeks ago called a surprise general election.