LONDON — In the midst of a messy political crisis at home over Britain’s impending exit from the European Union, Prime Minister Theresa May revealed Sunday that Donald Trump gave her this piece of advice: Sue the EU, don’t negotiate.

A bemused May turned him down. But the exchange was the latest example of the awkward dance between the U.S. and Britain, with the two leaders attempting to put on a public show of friendliness despite clear strains over trade, the EU and their approaches to diplomacy.

Trump told reporters on Friday that he had given May advice about how to deal with the EU that she found too “brutal.”

Asked in a BBC interview Sunday what that was, May responded with an amused expression: “He told me I should sue the EU. Not go into negotiation, sue them.”

With a laugh, she added: “Actually, no. We’re going into negotiations with them.”

In the past few days, Trump’s first official visit to Britain has been steered wildly off course by a series of humiliating remarks he has made about May’s leadership — especially her handling of the tense Brexit negotiations.

In an explosive interview with The Sun newspaper published Thursday — just as May was hosting Trump at a lavish black-tie dinner — Trump said the British leader’s approach likely “killed” chances of a free-trade deal with the United States. He said he had told May how to conduct Brexit negotiations, “but she didn’t listen to me.”