Juncker, reportedly, told May during a recent dinner party that the Brexit negotiations will not start until London pays the "divorce bill".
Ahead of the final round of France's presidential election and the pending Brexit negotiations with the United Kingdom, the president of the European Commission chose to give a speech in Italy on Friday in French instead of English.
The president of the European parliament, Antonio Tajani, told the Florence conference that no one was looking to undermine May, who says she called the snap election to strengthen her hand in the Brexit negotiations.
The negotiating directives stipulate that Britain would have to honour all its EU budget commitments made under the 2014-2020 financial period and "fully cover" all costs related to the relocation of the European Medicines Agency and the European Banking Authority.
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".
In an attempt to avoid a tit-for-tat response, European Council President Donald Tusk called on both parties to treat one another with "respect" on Thursday (4 May).
Speaking to an audience of European diplomats and experts in Florence, Jean-Claude Juncker also described the UK's decision to leave the EU as a tragedy. People get excited whenever we have elections.
Earlier, Mr Juncker's spokesman Margaritis Schinas brushed off Mrs May's comments, telling reporters: "We are not naive".
"But what's clear from Theresa May's reaction is that she is prepared, whatever the commission officials are doing in Brussels, to stand up for Britain's vital national interest in these very complicated talks".
"In the past, the European Union has done a little too much, even the Commission: too many rules, too much interference in the daily lives of our citizens".
"Britain's negotiating position in Europe has been misrepresented in the continental press".
May officially informed the European Union of the United Kingdom electorate's wish to withdraw from the bloc on March 29, which sparked a two-year period of Brexit negotiations.
John McDonnell, the right-hand man of Labour leader Jeremy Corbyn, said the results were not "the wipeout people had expected". As prime minister, she has also drawn a red line over the European Court of Justice maintaining jurisdiction over the United Kingdom post-Brexit. May said Wednesday: "Threats against Britain have been issued by European politicians and officials". Of course we will negotiate with our British friends in full transparency.
"We are very busy and we will not Brexitize our work", he said.