The president was critical of Brexit negotiations but says the US will stay out of Britain’s talks over its exit from the EU

Donald Trump has renewed his criticism of Theresa May’s handling of Brexit, claiming that she ignored his advice on how to negotiate and now “it’s tearing a country apart”.

The US president, a self-anointed master deal maker, also insisted that a second referendum on Britain’s departure from the European Union would be “unfair” and said he looks forward to making a bilateral trade agreement.

Trump, who is friendly with the former UK Independence party leader Nigel Farage, has long been a cheerleader for Brexit and alive to its domestic parallels. During his presidential election campaign in 2016, he tweeted: “They will soon be calling me MR. BREXIT!”

Speaking in the Oval Office alongside the Irish prime minister, Leo Varadkar, on Thursday, Trump said: “It’s a very complex thing right now, it’s tearing a country apart, it’s actually tearing a lot of countries apart and it’s a shame it has to be that way but I think we will stay right in our lane.”

Last summer, during a visit to the UK, Trump told the Sun newspaper that he told Theresa May “how to do” Brexit but “she didn’t listen to me”. May has previously indicated that Trump told her to “sue the EU” and “not go into negotiations”.

Trump said on Thursday: “I’m surprised at how badly it’s all gone from the standpoint of a negotiation. I gave the prime minister my ideas on how to negotiate it and I think you would have been successful.

“She didn’t listen to that and that’s fine – she’s got to do what she’s got to do. I think it could have been negotiated in a different manner, frankly. I hate to see everything being ripped apart now.”

May and Trump’s dialogues are a study in contrasting styles, with May preferring to work through bullet points, and Trump opting for freewheeling and dwelling on his achievements. But their relationship is said to have steadily improved, whereas Trump’s interactions with France’s president, Emmanuel Macron, tend toward soaring highs and jarring lows.

On the prospect of a second Brexit referendum, Trump said: “I don’t think another vote would be possible because it would be very unfair to the people that won. They’d say: ‘What do you mean, you’re going to take another vote?’ So that would be tough.

“I thought it would happen, it did happen, and both sides are very, very cemented in. It’s a tough situation. It’s a shame. There was no reason for that to happen. They could have had the vote and it should have gone smoothly and unfortunately it didn’t.”

UK MPs voted in favour of extending Article 50 beyond its 29 March deadline on Thursday. Earlier in the day, Trump said he believed Brexit was likely to be delayed. “I think they are probably going to have to do something because right now they are in the midst of a very short period of time – the end of the month – and they are not going to be able to do that.”

If and when the UK leaves the EU, it will negotiate its own trade deals, including with the US, for the first time in decades. Trump said: “We are talking with them about trade and we can do a very big trade deal with the UK.”

Turning to Varadkar, visiting the White House to celebrate St Patrick’s Day, he said: “Leo, I’m sure you agree on that. Would you like to express your feelings on Brexit? Maybe I shouldn’t let you do it, I’ll just get you in trouble.”

The taoiseach replied: “We have a different opinion, Mr President. I regret that Brexit’s happening.”

Varadkar said Brexit should not affect Northern Ireland, and that he would like to see a trade deal cemented between the EU and the US. “I think it will be a few years until the United Kingdom sorts itself out, but in the meantime the European Union is available to talk trade with the US.”

American presidents have been unable to resist dipping into Brexit. In April 2016, Barack Obama visited London and made an impassioned plea to Britons to remain in the EU, warning that the UK would be at the “back of the queue” in any trade deal with the US.

Trump has often relished taking positions opposite to Obama and his election campaign was a political cousin of Brexit with similar anti-immigration and anti-elite themes.

Last year, Trump claimed that he was at his golf course in Scotland “the day before Brexit” and correctly predicted the result of the referendum. In truth, he arrived a day later and welcomed the result, saying: “I said this was going to happen, and I think that it’s a great thing. Basically they took back their country.”

The White House is known to contain some strong Brexit supporters who admire May’s tenacity, although many in the US business community are baffled and bemused. Earlier on Thursday, Trump had tweeted: “My Administration looks forward to negotiating a large scale Trade Deal with the United Kingdom. The potential is unlimited!”

Liam Fox, the British trade minister, responded: “Greater trade between us reinforces a comprehensive alliance that goes far beyond the economic, providing for our national security and bringing prosperity to our people.”

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The US trade representative’s office has said it will launch negotiations with Britain after its exit from the EU. Last month, it laid out its objectives for a deal that included reduced tariff and non-tariff barriers for US industrial and agricultural goods.

The UK has not yet published its own negotiating mandate, which will probably take a couple of months and a possible parliamentary date. If Brexit goes ahead on schedule, negotiations could begin around September but it will be difficult to complete them before the end of next year, when a presidential election will sow fresh uncertainty. Among the British priorities would be an agreement to sell more military hardware to the Pentagon.