European Council President Donald Tusk has spoken of a "special place in hell" for "those who promoted Brexit without even a sketch of a plan of how to carry it out safely".
He was speaking after talks with Irish premier Leo Varadkar in Brussels.
Brexit-backing MPs reacted with anger to the comments, accusing Mr Tusk of "arrogance".
Downing Street said it was a question for Mr Tusk "whether he considers the use of that kind of language helpful".
The prime minister's official spokesman said: "We had a robust and lively referendum campaign in this country. In what was the largest democratic exercise in our history people voted to leave the EU."
He added that everyone should now focus on delivering that.
Mr Tusk's Twitter account tweeted his comments immediately afterwards:
And at the end of their press conference, Mr Varadkar was picked up by the microphones telling Mr Tusk: "They'll give you terrible trouble in the British press for that."
Mr Tusk nodded at the comment and both laughed.
Former UKIP leader, and now an independent MEP, Nigel Farage, tweeted back at Mr Tusk: "After Brexit we will be free of unelected, arrogant bullies like you and run our own country. Sounds more like heaven to me."
Commons leader Andrea Leadsom, who also campaigned for Britain's exit from the EU, said Mr Tusk should apologise for his "disgraceful" and "spiteful" comments.
"I'm sure that when he reflects on it he may well wish he hadn't done it," she told BBC Radio 4's World at One.
The Democratic Unionist Party's Brexit spokesman Sammy Wilson said: "This devilish Euro maniac is doing his best to keep the United Kingdom bound by the chains of EU bureaucracy and control.
"It is Tusk and his arrogant EU negotiators who have fanned the flames of fear in an attempt to try and overturn the result of the referendum."
But Sinn Fein President Mary Lou McDonald backed Mr Tusk, arguing that it was the position of "hardline" Brexit-supporting MPs like Boris Johnson and Jacob Rees-Mogg that was "intemperate" and "untenable".
"They are people who have acted with absolute contempt for [Ireland], utter disregard for the experiences of Irish people, north and south, with utter disregard for the peace process that has been collectively built over decades," she added.
Mr Tusk began his remarks by telling reporters there were 50 days to go until the UK's exit from the European Union.
"I know that still a very great number of people in the UK, and on the continent, as well as in Ireland, wish for a reversal of this decision. I have always been with you, with all my heart.
"But the facts are unmistakable. At the moment, the pro-Brexit stance of the UK prime minister, and the Leader of the Opposition, rules out this question.
"Today, there is no political force and no effective leadership for Remain. I say this without satisfaction, but you can't argue with the facts."
Theresa May - who supported the UK staying in the EU during the 2016 EU referendum but has always insisted that Brexit must be delivered because that was what people voted for - is due to arrive in Brussels on Thursday to seek legal changes to the withdrawal deal she signed with the EU. She hopes these changes will help her get it through the UK Parliament.
Mr Tusk said that the other 27 EU members had decided in December that the withdrawal agreement was "not open for renegotiation".
He said: "I hope that tomorrow we will hear from Prime Minister May a realistic suggestion on how to end the impasse.... following the latest votes in the House of Commons."
Mr Tusk said the Irish border issue and the need to preserve the peace process remained the EU's "top priority".
"The EU is first and foremost a peace project," he said. "We will not gamble with peace or put a sell-by date on reconciliation. This is why we insist on the backstop."
In a message to Mrs May, Mr Tusk said: "Give us a deliverable guarantee for peace in Northern Ireland and the UK will leave the EU as a trusted friend.
"I hope that the UK government will present ideas that will both respect this point of view and at the same time command a stable and clear majority in the House of Commons.
"I strongly believe that a common solution is possible and I will do everything in my power to find it."
Mr Varadkar said that while he was "open to further discussions" with the UK government about post-Brexit relations the legally-binding withdrawal agreement remained "the best deal possible".
He said he had agreed with Mr Tusk that the backstop was "needed as a legal guarantee to ensure that there is no return to a hard border on the island of Ireland while protecting the integrity of our European single market and customs union".
He added that he had agreed with Mr Tusk that "in light of the ongoing uncertainty in London and the fast-approaching deadline" preparations for a no-deal Brexit must intensify.