European Council President Donald Tusk, who will oversee the negotiations that will take Britain out of the EU, said on Wednesday he wanted other member states to be fair towards London, while retaining their unity.
"I want to wish him luck as I know he will leave nothing to chance", Juncker said.
The remarks emerged as the European Parliament met to discuss last month's Special European Council in which leaders of the EU 27 formally endorsed the bloc's negotiating strategy for Brexit talks, set to commence after the UK General Election.
In line with negotiator Michel Barnier, most MEPs emphasised the unity between the European Union institutions and the 27 Member States, who are determined to act together to reach a balanced agreement with the United Kingdom.
Nigel Farage has accused Jean-Claude Juncker of attempting to "bully the Brits" over Brexit negotiations.
Mr Juncker reportedly commented that he was "10 times more sceptical" of the likelihood of a successful Brexit after the Downing Street meeting with the Prime Minister.
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He described a situation in which the details of confidential conversations were "blabbed to an opposition newspaper", adding: "And then a few days later, in a display of extreme petulance, you even deride the national language of the host - which, by the way, is looking a bit silly because last Saturday's extravaganza knowns as the Eurovision Song Contest saw 90% of the songs sung in English".
The Brexit negotiation "is now in the hands of our capable divorce lawyers", said European Commission head Jean-Claude Juncker, who also addressed MEPs, in reference to the EU's chief negotiator Michel Barnier. "I doubt it, because in any part of the civilized world frankly that behavior would be considered to be bloody rude and the act of a bully".
MEPs also praised what they see as the defeat of populist forces across Europe in elections, such as in the Netherlands and France, since the Brexit vote. "For good reason people are very critical of the European Union, but they don't want to do what the United Kingdom did, [they] don't want to leave the European Union", liberal leader Guy Verhofstadt said, urging reform.
"And I think that it didn't happen by accident". The Dutch didn't want a "Nexit".
President of the European Council, Donald Tusk, said negotiations would take place with a phased approach and that citizens' rights, financial commitments from the United Kingdom and free-trade agreements would be key. "The process shows how united and prepared the European Union will be".
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