Theresa May has congratulated Donald Trump on taking office as US president - and says she looks forward to meeting him in Washington.
The prime minister stressed her belief he was committed to advancing the "special relationship" with the UK.
But Mrs May told the Financial Times she expects "very frank" talks on areas where their opinions seem to differ such as the EU and Nato.
The PM said she hoped for early progress on a US-UK trade agreement.
Mrs May said she believed Mr Trump "recognises the importance and significance of Nato", despite him being quoted earlier in the week as describing the military alliance as "obsolete".
"I'm also confident the USA will recognise the importance of the co-operation we have in Europe to ensure our collective defence and collective security," she told the FT.
Mr Trump also said recently he did not really care if the EU separated.
Mrs May, who this week outlined for the first time her plan for Brexit, said: "The decision taken by the UK was not a decision about breaking up the EU.
"I want the EU to continue to be strong and I want to continue to have a close and strategic partnership with the EU. It is important for security issues. With the threats we face it's not the time for less co-operation."
'Front of the line'
Mr Trump was sworn-in as the 45th US president on Friday.
In a statement issued after the inauguration, Mrs May said: "From our conversations to date, I know we are both committed to advancing the special relationship between our two countries and working together for the prosperity and security of people on both sides of the Atlantic.
"I look forward to discussing these issues and more when we meet in Washington."
In her FT interview, Mrs May said she was "confident we can look at areas even in advance of being able to sign a formal trade deal".
But despite Mr Trump's indication he backed a quick post-Brexit trade deal, there was a heavily protectionist tone in the inauguration speech.
Some Labour MPs questioned how the prime minister's aim of a free trade deal with the US would be possible given the "America first" strategy outlined by Mr Trump.
David Lammy tweeted: "Every decision on trade will be made to benefit Americans. Hmm - looking forward to this trade deal, then."
Chris Bryant said: "I'm not sure a UK trade deal with Trump will be very mutually beneficial."
However, speaking to the BBC in Myanmar, also known as Burma, Foreign Secretary Boris Johnson said there was every reason to "be positive and optimistic" about a trade deal.
"I think the new president has made it very clear that he wants to put Britain at the front of the line... and obviously that's extremely exciting and important".
Earlier Mr Johnson offered his own "warmest congratulations" to Mr Trump.
He said the UK would "work hand in glove for the stability, the prosperity and the security of the world".
Meanwhile, Thousands of women are expected to join a march in London later as part of an international protest campaign on the first full day of Mr Trump's presidency.
Churchill bust returns
Mr Trump has appeared to make good on a pledge to return a bust of Sir Winston Churchill to the White House's Oval Office.
The sculpture of the World War Two prime minister's face is said to be a replica of one given to President Lyndon B Johnson in the 1960s and first appeared in the Oval Office during George W Bush's administration in 2001.
The presence of the Churchill bust was noticed as Mr Trump signed his first orders as president.
A report that the bust of Dr King no longer remained in the Oval Office was later found to be discredited.