British Foreign Secretary Boris Johnson has caused controversy by comparing French President Francois Hollande to a World War II camp guard administering "punishment beatings".
His comment - during an official visit to India - was condemned as "abhorrent" by the European Parliament's chief Brexit negotiator Guy Verhofstadt.
The British Labour party said it was "wild and inappropriate" and Liberal Democrat leader Tim Farron denounced it as "utterly crass".
But Mr Johnson was defended by Downing Street, who said he continued to enjoy the full confidence of Prime Minister Theresa May.
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The row came as Labour leader Jeremy Corbyn accused Ms May of "demeaning" her office and her country by threatening to make the UK an offshore tax haven if she cannot get the Brexit deal she wants from the EU.
— Jeremy Corbyn MP (@jeremycorbyn) January 18, 2017
And EU leaders warned that Ms May faces an "arduous task" to negotiate the new relationship with Europe that she outlined in her keynote speech setting out her plans for Brexit yesterday.
European Council president Donald Tusk said that Ms May's decision to take Britain out of the European single market showed that London had "finally understood and accepted" the EU's position on freedom of movement.
And Mr Tusk said he hoped she would now also accept that the UK cannot "pick and choose" in the upcoming negotiations.
In response to comments from an aide to Mr Hollande, who said Britain should not expect a better trading relationship from outside the EU, Mr Johnson warned Europe against a punitive approach to the Brexit talks.
"If Monsieur Hollande wants to administer punishment beatings to anyone who chooses to escape, rather in the manner of some World War Two movie, then I don't think that's the way forward," he said.
"It's not in the interests of our friends or our partners."
Mr Verhofstadt, a former Belgian prime minister and senior MEP, said the Foreign Secretary's comments were "deeply unhelpful" and urged Mrs May to condemn them.
But the PM's spokeswoman dismissed the row as "hyped-up" and said Mr Johnson had been doing no more than using "theatrical" language.
"He was making a point," she said. "He was in no way suggesting that anyone was a Nazi."
Ms May clashed with Mr Corbyn at Prime Minister's Questions in the House of Commons over her suggestion that the UK was ready to adopt a new low-corporation tax, low-regulation model to attract business and investment from elsewhere in the world if it was unable to strike a favourable deal with the EU.
Mr Corbyn called on the PM to "stop her threat of a bargain basement Britain, a low-pay tax haven on the shores of Europe".
The Singapore-style model - which Labour suggested was the favoured outcome of some Conservative Cabinet ministers - "wouldn't necessarily damage the EU, but it would certainly damage this country - businesses, jobs and public services", said Mr Corbyn.
"She demeans herself and her office and our country's standing by making these kinds of threats."
But Ms May denied her Brexit plan was based on threats, insisting she had set out a vision for "a stronger, fairer, more united, more outward-looking, prosperous, tolerant and independent, truly global Britain".
And Mr Tusk acknowledged that Ms May had offered "warm" support for a successful future EU, describing her stance as closer to that of Sir Winston Churchill than US President-elect Donald Trump.