- Video report by ITV News Political Editor Robert Peston
Donald Trump is "100% behind Nato", Theresa May has said following their first meeting.
In the past, Mr Trump has described the organisation as "obsolete" and questioned the contribution of some members.
But speaking at the White House today, Mrs May told a joint press conference: "Today we have reaffirmed our unshakeable commitment to this alliance. Mr President, I think you confirmed that you are 100% behind Nato."
During the press conference:
- Mrs May revealed the president had accepted an invitation to make a state visit to the UK later this year
- Mr Trump hailed the "special relationship" between the two countries as "one of the great forces in history"
- The president said he would allow decisions on torture to be made by his defence secretary James Mattis
- And Mr Trump said Brexit would be a "wonderful thing" for the UK
Mrs May is the first world leader to meet with Mr Trump following his inauguration last week.
Following talks in the Oval Office, Mr Trump hailed the "special relationship" between the UK and US as one of the "great bonds" - and pledged his support to it.
He said: "The special relationship between our two countries has been one of the great forces in history for justice and peace.
"Today the US renews our deep bond with Britain - military, financial, cultural and political."
He continued: "We pledge our lasting support to this most special relationship.
"Together, America and the United Kingdom are a beacon for prosperity and the rule of law."
The prime minister said that, among other things, the two leaders had agreed on the need to "eradicate" so-called Islamic State and radical Islamic ideology.
She said that President Trump had also reasserted his support for NATO.
"We are united in our recognition of NATO as the bulwark of our collective defence - today we have reaffirmed our unshakeable commitment to this alliance," she said.
After their highly-anticipated meeting on Friday, Mr Trump claimed the UK-US relationship had "never been stronger."
He revealed that the two countries were looking to strengthen their mutual ties, including business, commerce and foreign affairs.
Mrs May congratulated the President on his "stunning" election victory in November, and said that there was "much" on which the two leaders had agreed.
The Prime Minister revealed that she had extended an invitation from the Queen for the President to make a state visit to the UK later this year, which Mr Trump had accepted.
Speaking of her visit to Washington, she said: "The invitation is an indication of the strength and importance of the special relationship that exists between our two countries.
"A relationship based on the bonds of history, of family, kinship and common interests."
Mrs May also appeared confident that a post-Brexit trade deal could be struck between the US and UK.
She added that high-level trade talks could be in the offing very quickly.
"I think the President and I are ambitious to build on this relationship in order to grow our respective economies, provide the high-skilled and high-paid jobs of the future for working people across America and the UK," she said.
Mrs May added: "I'm convinced that a trade deal between the US and the UK is in the national interests of both countries and will cement the crucial relationship that exists between us - particularly as the UK leaves the EU and reaches out to the world."
The President reiterated that Brexit was an "example of things to come," adding that it was going to be a "wonderful thing".
"When it irons out you are going to have your own identity," he said.
"You are going to have the people that you want in your country, and you are going to be able to make free-trade deals without somebody watching you and what you're doing."
Mr Trump was challenged about his support for torture and insisted that he would allow decisions to be made by his defence secretary James Mattis - who has different views on the issue.
Explaining his position on torture, Mr Trump said: "We have a great general who has just been appointed secretary of defence, general James Mattis and he has stated publicly that he does not necessarily believe in torture or waterboarding - or however you want to define it. Enhanced interrogation would be words that a lot of people would like to use.
"I don't necessarily agree but he will override because I am giving him that power. He is an expert, he is highly respected, he is the general's general."
Speaking of Russia, President Trump said he hoped for a "fantastic" relationship with Vladimir Putin.
He said the two countries could strengthen their bonds if they united in the goal to defeat so-called Islamic State.
President Trump warned that it was "very early" to be talking of loosening sanctions imposed by the US on Russia, but said he looked forward to having a "great relationship with all countries."
Mrs May added that the UK believed the sanctions should continue.