President Donald Trump said the United States and Britain could agree a "phenomenal" post-Brexit trade deal.

"As the UK makes preparations to exit the European Union, the United States is committed to a phenomenal trade deal between the US and the UK," Trump told a joint news conference with U.K. Prime Minister Theresa May on Tuesday during his state visit to London.

He added: "There is tremendous potential in that trade deal - I say probably two and even three times of what we are doing right now."

Trump said the two countries could do two to three times that amount of trade they're currently conducting.

May has been dogged by her failure to achieve Brexit and is stepping down this week as head of her Conservative Party but will remain as prime minister until her successor is chosen. It will be the new prime minister's responsibility to achieve Brexit and any bilateral trade deal with the U.S.

The collapse of May's premiership over Brexit had raised concerns that Trump might publicly humiliate May during his visit.

Instead, Trump steered clear of rhetoric that could embarrass her and glossed over even the most sensitive issues such as Huawei and her succession.

Trump mentioned Boris Johnson, who has said the United Kingdom should leave the European Union on Oct. 31, deal or no deal, and Jeremy Hunt, Britain's foreign minister who has warned against leaving without a deal.

"I know Boris, I like him, I've liked him for a long time. I think he would do a very good job," Trump told reporters at a news conference beside May at Britain's Foreign Office.

"I know Jeremy, I think he'd do a very good job," he added.

When asked if an interim decision by British ministers to allow Huawei a limited role in 5G networks would affect security cooperation with Britain's biggest ally, Trump said he would work out the issues.

"We have an incredible intelligence relationship and will be able to work out any differences," Trump said.

"We did discuss it, I see absolutely no limitations, we have never had limitations, this is a truly great ally and partner and we will have no problem with that," he said.

The Trump administration has told allies not to use Huawei's 5G technology and equipment because it fears that would allow China to spy on sensitive communications and data. Huawei denies it is, or could be, a vehicle for Chinese intelligence.

Trump's state visit, promised by May back in January 2017 when she became the first foreign leader to meet him after he took office, has been cast as a chance to celebrate Britain's "special relationship" with the United States, boost trade links and reaffirm security cooperation.

On Brexit, Trump said Britain's EU divorce would happen.

"I would say ... I would think it will happen and it probably should happen. This is a great, great country and it wants its own identity, it wants to have its own borders, it wants to run its own affairs. This is a very, very special place.

"As the UK makes preparations to exit the European Union, the United States is committed to a phenomenal trade deal between the US and the UK," Trump said.

He said he had refused to meet opposition Labour Party leader Jeremy Corbyn, a veteran socialist who criticized Trump at a protest in central London on Tuesday.

Trump said Queen Elizabeth was a "fantastic woman" and thanked Britain for the state visit which he said had cemented the greatest alliance the world had ever known.

May praised the "precious and profound" alliance between the United States and the United Kingdom but said friends could also be open where they disagreed — such as on the Iran nuclear deal and the Paris climate agreement.

The U.K. still supports an international agreement to curb Tehran's nuclear ambitions, but Trump has withdrawn the U.S. from the deal.

May also told the nationalist president that "cooperation and compromise are the basis of strong alliances."

This report contains material from Reuters and The Associated Press.