Boris Johnson has compared the EU's aims to Hitler's, saying both involved the intention to unify Europe under a single "authority".
The pro-Brexit Tory MP said both the Nazi leader and Napoleon had failed at unification and the EU was "an attempt to do this by different methods".
Shadow foreign secretary Hilary Benn, who backs Remain, said the comparison was "offensive and desperate".
Meanwhile, UKIP leader Nigel Farage has backed Mr Johnson to be the next PM.
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Mr Farage told the Mail on Sunday he was a "Boris fan" and said he was backing the former London mayor to succeed David Cameron, if the prime minister resigned following the EU referendum.
The referendum takes place on 23 June, when voters in the UK will be asked whether they want the country to stay in or leave the European Union.
Speaking to the Sunday Telegraph, Mr Johnson said European history had seen repeated attempts to rediscover the "golden age of peace and prosperity under the Romans".
"Napoleon, Hitler, various people tried this out, and it ends tragically. The EU is an attempt to do this by different methods," he said.
"But fundamentally what is lacking is the eternal problem, which is that there is no underlying loyalty to the idea of Europe.
"There is no single authority that anybody respects or understands. That is causing this massive democratic void."
'Divisive politics'
Rejecting Mr Johnson's analysis, Mr Benn said: "Leave campaigners have lost the economic argument and now they are losing their moral compass."
Former Labour minister Yvette Cooper, who supports the Remain campaign, accused Mr Johnson of a "shameful lack of judgement" and a willingness to play "the most divisive, cynical politics".
She added: "He should not try to play political games with the darkest and most serious chapter of Europe's history. The EU has played a critical role keeping peace in Europe ever since."
But Tory Leave campaigner Jacob Rees-Mogg said Mr Johnson's comments were "absolutely true".
He said Hitler and Napoleon "wanted to create a single European power... by force. And the EU is trying to do it by stealth."
Asked on the BBC's Andrew Marr Show about her views on the referendum campaign, Tory MP and Vote Leave campaigner Andrea Leadsom said Bank of England governor Mark Carney had made "an incredibly dangerous intervention" three days ago.
She said his comments that a vote to leave could hit the UK economy were "purely speculative".
"They [the Bank] are not there to promote financial instability and that is what they have done," she said.
Also appearing on Marr, Mr Carney defended his comments, saying he has "absolutely not" overstepped the mark.
"I understand there's a lot of passion on all sides of this debate. Central banking isn't a passionate business... it's analytic, it's evidence-based," he said.
"And the judgements we take - and I would emphasise we... are carefully considered and only reflect our remits, our mandates."
'Disappointing'
Northern Ireland First Minister Arlene Foster, who backs Leave, told Marr Mr Carney's remarks on Thursday were "rather surprising".
She also rejected suggestions that leaving the EU could harm relations with the Republic of Ireland or damage the peace process.
"I'm not worried at all, because the peace process is not built on the European Union," she said, adding that it had been "disappointing" to see former Foreign Secretary William Hague suggest there could be a negative impact.
Ms Foster said leaving the EU would free Britain and Northern Ireland from the bloc's "overreaching bureaucracy".
Campaigning in Oxfordshire on Saturday, Mr Cameron warned that leaving the EU would have a "devastating impact" on funding for infrastructure projects.
Labour leader Jeremy Corbyn, who also backs Remain, told ITV's Peston on Sunday he wanted an EU that was "a unity of people of the left... collectively working for a better standard of living across Europe".
Asked how he and Mr Cameron could have such different views yet both support Remain, he said people should "listen to both of us and make up their minds".
But he said the two were unlikely to share a platform. "I don't think it would work," he said.
Mr Farage, who is due to take part in a debate with Mr Cameron, told Peston he could understand why the prime minister was unwilling to do so with a pro-Brexit Conservative minister.
He said Mr Cameron feared "it could lead to divisions [in the Tory party] that could never be mended".
With less than six weeks to go until the vote, polls have put the Remain and Leave campaigns at roughly 50-50.