Transatlantic tensions over the British ambassador’s leaked criticisms of Donald Trump have grown into a diplomatic crisis after the US president attacked Sir Kim Darroch as “a pompous fool” and his commerce secretary postponed planned trade talks with Liam Fox.

A day after Trump said he would no longer deal with Darroch following the release of UK diplomatic memos calling him “incompetent”, “inept” and “insecure”, he used his Twitter feed to attack the diplomat, who he described as “wacky” and “very stupid”.

The president also volleyed a series of insults at Theresa May, calling her “foolish” and saying her Brexit plan had been a disaster because she ignored his advice.

The controversy escalated further as Jeremy Hunt, the foreign secretary and Conservative leadership candidate, responded by calling the president’s language “disrespectful and wrong”.

In Tuesday night’s Conservative leadership debate, Hunt reiterated his support for Darroch and said that he would keep him in place were he to become prime minister. Frontrunner Boris Johnson was more limited in his criticism of Trump, saying that a good relationship with the US was “of fantastic importance”. And he refused to say that he would back Darroch if he won the contest.

The difficulty of the ambassador’s position had become clear earlier when he withdrew from a White House meeting he was due to attend in Washington with Fox, the international trade secretary, and Trump’s daughter and adviser Ivanka.

A government source said that after the meeting went ahead with no mention of the controversy and no apology from Fox, a later session with the commerce secretary, Wilbur Ross, was abruptly called off.

A British government source claimed that the cancellation was the result of “a diary clash” on Ross’s side while a US commerce department spokesperson said: “The department is working to reschedule today’s meeting to a mutually agreeable time.”

Despite Trump’s refusal to deal with Darroch any more, Hunt, who is up against Boris Johnson in the race to succeed May, said he would keep the ambassador in place if he were to become prime minister. Downing Street also offered Darroch its full support, describing him as “a highly respected and dutiful public servant” who had the prime minister’s full confidence.

But Trump’s repeated criticisms, the latest of them issued in his now familiar early morning tweets, have deepened the sense that Darroch’s role may become untenable.

In messages posted shortly before 8am, Trump again condemned Darroch and renewed his criticism of the prime minister over her Brexit negotiations, which he had praised on his state visit to the UK just over a month ago.

“The wacky ambassador that the UK foisted upon the United States is not someone we are thrilled with, a very stupid guy,” Trump wrote. “He should speak to his country, and Prime Minister May, about their failed Brexit negotiation, and not be upset with my criticism of how badly it was handled.

“I told her how to do that deal, but she went her own foolish way – was unable to get it done. A disaster! I don’t know the ambassador but have been told he is a pompous fool. Tell him the USA now has the best economy and military anywhere in the world, by far and they are both only getting bigger, better and stronger.”

In response to that attack, Hunt said: “[Donald Trump], friends speak frankly so I will: these comments are disrespectful and wrong to our prime minister and my country. Your diplomats give their private opinions to [Mike Pompeo, the US secretary of state], and so do ours!

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“You said the UK/US alliance was the greatest in history and I agree but allies need to treat each other with respect as Theresa May has always done with you. Ambassadors are appointed by the UK government and if I become PM our ambassador stays.”

The row began when the Mail on Sunday printed extracts of confidential memos in which Darroch issued wide-ranging criticisms of Trump’s administration. The US president gave a relatively measured response on Sunday saying he was not a big fan of Darroch, but then announced on Monday he would no longer deal with the ambassador.

Donald J. Trump (@realDonaldTrump) The wacky Ambassador that the U.K. foisted upon the United States is not someone we are thrilled with, a very stupid guy. He should speak to his country, and Prime Minister May, about their failed Brexit negotiation, and not be upset with my criticism of how badly it was...

In a pointed riposte to Trump’s criticisms of May’s Brexit negotiations, May’s spokesman noted the president’s comments at a joint press conference during his state visit to the UK “in which he said she brought the negotiations to a very good point, and that the PM deserved a lot of credit. And as you know, nothing further has happened in the Brexit negotiations since then.”

The spokesman declined to say why Darroch was not accompanying Fox to the White House, saying the ambassador was “supporting Liam Fox on his trip in other ways”. It is understood Darroch took the decision himself to avoid putting Ivanka Trump in a difficult position.

Darroch has been prevented by Trump from attending a dinner for the Emir of Qatar, but the Foreign Office was reassured this was a one-off, and it does not denote he is being debarred from future events or meetings.

Hunt is understood to believe the next British ambassador to Washington should be a career diplomat, since to do otherwise would probably be seen to be giving a victory to the leakers. Washington was not named as one of the postings that should be open to outside appointments, Foreign Office sources also pointed out.

The foreign secretary has been in touch with Darroch to offer his personal support, and there has been no discussion of him leaving his post early.

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On Tuesday morning, May gave the same message to the weekly meeting of her cabinet, condemning the leak to the Mail on Sunday as “utterly unacceptable”.

Describing May’s words to cabinet, her spokesman said: “The prime minister said that while at the same time the views expressed in the documents are not necessarily the views of ministers or the government, it is hugely important that ambassadors are able to provide honest, unvarnished assessments of the politics in their country. She said it is therefore absolutely right that we continue to give Sir Kim Darroch our full support.”