The Prime Minister insisted he would visit Britain despite a new round of criticism.
Mrs May was challenged by the BBC's Andrew Marr to say whether she recognised claims Mr Trump was like a 'child' and not equipped to be President.
The premier visibly grimaced as she was asked the question but stood by her ally.
Mr Trump has been reduced to tweeting that he is a 'very stable genius' after an incendiary new book claims he is incapable of fulfilling his duties.
Mrs May told Marr: 'I do - obviously I've worked with President Trump on a number of issues as we continue to work with the United States on a number of issues. President Trump I think (..).
'What I make of him is somebody who is taking decisions on what he believes is in the best interests of the United States.
'You know, the United Kingdom government and I will take decisions here on what we believe is in the best interests of the UK.'
Marr went on: 'In the States there are quite serious questions being raised by some people about his mental state. Do you think they're serious?'
She replied: 'No. As I say when I deal with President Trump what I see is somebody who is committed to ensuring that he is taking decisions in the best interests of the United States.'
She added: 'He will be coming to this country.'
American journalist Michael Woolf published the extraordinary claims this week in Fire and Fury: Inside the Trump White House.
Award-winning political writer Mr Wolff, 64, said he had been 'astounded' by the global impact of his book, which was based on months inside the White House West Wing and interviews with more than 200 people, including Mr Trump and his former chief strategist Steve Bannon.
The White House has described the book as 'complete fantasy'. After a failed last-ditch legal bid to ban its publication, Mr Trump yesterday maintained his Twitter war of words with Mr Wolff, branding him a 'total loser'.
The comments were made by Mr Wolff in his first British newspaper interview since Mr Trump reacted with rage to the publication of Fire And Fury: Inside The Trump White House.
Speaking to The Mail on Sunday, Mr Wolff made fresh astonishing claims about the President's mental state, saying some officials believed the 71-year-old had learning disabilities or even dementia.
Others thought he could have Attention Deficit Hyperactivity Disorder (ADHD), a mental disorder often associated with children.
Mr Wolff revealed how Mr Trump is so ignorant about the UK that he 'had no idea what Brexit was' as late as two weeks before the referendum in 2016.
He warned Mrs May's controversial offer of a State visit to Britain, made weeks after Mr Trump was elected, could backfire.
It was seen as a bid to woo him into giving Britain a lucrative post Brexit Anglo-US trade deal.
But Mr Wolff claimed Mr Trump sees it purely as an opportunity to show off and outshine the Queen: 'He sees the Queen in reality TV show terms. That's the Trump modus operandi. He will try to Trumpalise the Queen and Buckingham Palace.'
And there could be more trouble if he is not on the guest list for the Royal Wedding in May.
'He doesn't like being snubbed and wants to be the centre of attention all the time,' Mr Wolff said.
'Trump's foreign policy doctrine is simple: you Brits suck up to him and enlist in whatever geopolitical fantasy he has going, he'll give you what you want – though only if it doesn't hurt him. It is not so much vengeance, rather 'you flatter me and I'll flatter you.'
However, it is thought to be unlikely that Mr Trump will be invited to the wedding, not least because Prince Harry recently conducted a fawning interview with Barack Obama.