European Commission President Jean-Claude Juncker criticised Johnson for comparing the EU to Hitler and suggested that the former mayor of London visits Brussels.
Shortly afterwards, Juncker's chief of staff described the prospect of Johnson becoming UK Prime Minister as a "horror scenario".
Martin Selmayr appeared to compare Johnson with France's Marine Le Pen and US presidential candidate Donald Trump in a provocative tweet.
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The twin verbal attacks on Johnson sparked criticism by Brexit campaigners but, on Friday, the Commission made a robust defence of Juncker's intervention, telling this website the aim was to highlight the rise of populist movements in Europe which, it says, could cause "less stability, less consensus on issues such as trade or on how to deal with Russian aggression."
The row was triggered after Johnson, who is backing the Brexit campaign, earlier this month compared the EU's efforts to unify Europe with earlier attempts by Napoleon and Hitler.
Speaking on Thursday at the start of the G7 summit in Japan, Juncker said: "I'm reading in (the) papers that Boris Johnson spent part of his life in Brussels. It's time for him to come back to Brussels, in order to check in Brussels if everything he's telling British people is in line with reality. I don't think so, so he would be welcome in Brussels at any time."
Juncker says Johnson needs to be re-educated about the way the EU works.
Asked about Johnson's comments linking the EU to Hitler and whether he could work with him if he is made a minister in Prime Minister David Cameron's government, Juncker said the former mayor's image of the EU is out of touch with reality.
"The atmosphere of our talks would be better if Britain is staying in the EU," Juncker told reporters.
Juncker also hinted that if Britain's highest-profile campaigner were to become Prime Minister then his discussions with European partners might be strained.
Johnson, one of Britain's best known politicians and a favourite with bookmakers to succeed Cameron as Prime Minister, told the Sunday Telegraph newspaper on May 15 that the EU is an attempt "by different methods" to unite the continent under a single government. "Napoleon, Hitler, various people tried this out, and it ends tragically," he told the paper.
Johnson, who previously worked in Brussels as a journalist, hit back at the remarks by Juncker and Selmayr, telling Sky News, "I'm afraid what I am saying to the British people is in line with reality and if we vote to remain, which I sincerely hope we don't, then they will go on with measures that will take us further into a federal European super state.
"The whole exercise in Europe is now aimed at propping up the euro. That is the entire mission of the EU. They will try to create a fiscal union, a political union."
He said it all tended towards a mission for a "United States of Europe, into which Britain will be sucked".
The comments by Selmayr, a long-time aide to Juncker, in which he says "it is worth fighting populism", sparked a backlash among Out campaigners in Britain.
Vote Leave media spokesperson Robert Oxley said of Selmayr's intervention: "Unelected bureaucrat working for unelected bureaucrat speaks."
But, on Friday, a Commission spokesperson hit back, telling the Parliament Magazine, "The head of cabinet of the president did nothing else but to point to the fact that in four of the G7 members, populist movements may lead to the replacement of the current head of state or government before the next G7 - and that this would bring with it less stability, less consensus on issues such as trade or on how to deal with Russian aggression."
He pointed out that ahead of the next G7, there are referenda in the UK (June) and in Italy (October) as well as presidential elections in the US and in France.
The spokesman added, "It was a general remark on similar, though not identical phenomena and risks in the four G7 members concerned. The Commission, which is a member of the G7 since its inception, is interested in G7 stability and prosperity and in promoting the common G7 values."
Juncker also found an ally in Denis MacShane, a former Europe Minister in the UK, who told this website, "The plain fact is that Boris Johnson is incapable of distinguishing between fact and fiction, lies and truth when he writes or speaks on Brussels."
MacShane, who served in Tony Blair's administration said, "Every leader in Europe is worried about the populist surges from isolationists in many EU countries and Boris is the populist-in-chief in the UK, the English version of Donald Trump with the same hair-style. Boris is always attacking everyone who works in Brussels so it seems fair that now and then Brussels has a pop back."
European Council President Donald Tusk, also in Japan for the G7, also weighed in to the row, saying he would work with Johnson if he became a minister. It is the "European way" to cooperate with government ministers whatever their opinions, he said.
"We have to respect every democratic decision, the result of the referendum and the possible political consequences of the referendum," Tusk said. "I think it's quite normal to have normal relations with politicians and at the same time to have your own opinion about their opinions."
Jayne Adye, Campaign Director of leading cross-party, grassroots Eurosceptic group Get Britain Out, said, "It is no surprise the unelected bureaucrats of Brussels are now describing the hypothetical situation of Boris Johnson being elected Britain’s Prime Minister as a ‘horror scenario’. For many years those working for the EU have treated democracy with deliberate contempt. It is not Boris Johnson they believe is a ‘horror scenario’ it is the principle of democracy.
"The EU elites, with their chauffer driven cars and enormous salaries, think they are smarter than the public, and believe decisions should be taken by men in grey suits accountable only to other men in grey suits. The public are an irrelevance to them. This is why the European Commission is the Government of Europe and is not accountable to the people.
"We at Get Britain Out truly believe in democracy, as it is the fundamental right of every person in society to be able to hire and fire its politicians and leaders. The European Union is undemocratic to its very core, and I’m confident the Great British Pubic believe in democracy too, and therefore will vote to ‘Leave’ in the referendum on our EU membership on June 23. The real ‘horror scenario’ would be for the UK to remain in this unelected club of unaccountable elites."