Donald Tusk said Brexit negotiations will “become impossible” if the UK and the EU become embroiled in arguments before the formal talks have even begun.
Mrs May sent shock waves through Brussels with a dramatic Downing Street statement on Wednesday accusing unnamed “European politicians and officials” of issuing threats deliberately timed to affect the June 8 vote.
The row blew up after a German newspaper published an apparently well-briefed account of the Prime Minister’s meeting with key Brussels figures in No 10 last week.
It reportedly ended with European Commission president Jean-Claude Juncker saying he was “10 times more sceptical” of the likelihood of a successful Brexit.
In a call for calm, Mr Tusk appealed for discretion in the negotiations, a plea widely viewed as being aimed at Mr Juncker’s office.
At a press conference in Brussels, Mr Tusk said: “These negotiations are difficult enough as they are.
“If we start arguing before they even begin, they will become impossible.
“The stakes are too high to let our emotions get out of hand because at stake are the daily lives and interests of millions of people on both sides of the channel.
“We must keep in mind that in order to succeed we need today discretion, moderation, mutual respect and a maximum of goodwill.”
European Parliament president Antonio Tajani rejected the Prime Minister’s claim and a spokesman for Mr Juncker said his office was too busy to meddle in the election.
Mr Tajani said: “We are not seeking to influence the result in the UK.
“It is better to have an interlocutor who is not constantly looking for votes because they have had the election, in order to work towards a good solution ...”, he added.
“If you have an election campaign, the rhetoric gets sharper and more robust. I don’t think there is any question of influencing the campaign.”
Earlier, Mr Juncker’s spokesman Margaritis Schinas brushed off Mrs May’s comments, telling reporters: “We are not naive. We know that there is an election taking place in the United Kingdom. People get excited whenever we have elections.
“This election in the United Kingdom is mainly about Brexit. But we here in Brussels, we are very busy, rather busy, with our policy work.
“We have too much to do on our plate. So, in a nutshell, we are very busy. And we will not Brexitise our work.”
Speaking outside Number 10 on Wednesday, the PM said: “The events of the last few days have shown that, whatever our wishes and however reasonable the positions of Europe’s other leaders, there are some in Brussels who do not want these talks to succeed, who do not want Britain to prosper.
“Britain’s negotiating position in Europe has been misrepresented in the continental press. The European Commission’s negotiating stance has hardened.
“Threats against Britain have been issued by European politicians and officials.
“All of these acts have been deliberately timed to affect the result of the General Election that will take place on June 8.”
Norwegian prime minister Erna Solberg said that Brexit was “challenging” not only for the UK and EU but also for her country, whose biggest trading partner is Britain.
“We are, of course, very concerned about how the arrangements will be in the future between the EU and the UK ... We believe it is possible to find good arrangements in the future,” she said.