The US president, speaking in London at the start of the Nato summit, claimed he would "stay out" of the General Election campaign because he does not want to "complicate it".
It comes six months after he answered a question about the NHS during a previous visit to the UK, saying: "When you're dealing in trade, everything is on the table."
His comments today will ease fears at Conservative Party headquarters that Mr Trump's visit could derail Boris Johnson's election campaign. Labour has made the proposed US-UK trade deal a central theme of its campaign, and the controversial US President's unpopularity risks contaminating the Prime Minister if their close personal relationship is put on show this week.
Mr Trump did go on to describe Mr Johnson as "very capable" and said he would be meeting the Prime Minister during the course of his visit to the UK.
In a breakfast meeting with Nato Secretary General Jens Stoltenberg at the US ambassador's residence in London, Mr Trump was asked if the NHS should be on the table in trade talks.He replied: "No, not at all, I have nothing to do with it. Never even thought about it, honestly."
The president added: "I don't even know where that rumour started. We have absolutely nothing to do with it and we wouldn't want to if you handed it to us on a silver platter, we want nothing to do with it."
Labour leader Jeremy Corbyn published a letter to Mr Trump on Monday night in which he asked for "reassurances" that US negotiators would not look to push up UK medicine prices by seeking access to the NHS for major American pharmaceutical companies.
His party has repeatedly claimed that the health service is "on the table" in a post-Brexit trade deal with the US.
Mr Trump said he could "work with anybody" when asked whether he could work with Mr Corbyn as prime minister, though earlier said he thought Mr Johnson would do a "good job".
Leaders including Mr Trump and Mr Corbyn will gather for a reception at Buckingham Palace on Tuesday evening.
While steering clear of UK domestic politics, Mr Trump did ignite a fresh diplomatic row with French President Emmanuel Macron, accusing him of "insulting" Nato allies.
The US presiden said Mr Macron had been "very disrespectful" after he claimed in an interview that the alliance was "brain dead".
Mr Macron's attack followed Turkey's incursion against the Kurds in northern Syria without warning other Nato members - a move that alarmed other allies.
Speaking during a breakfast meeting with Nato secretary general Jens Stoltenberg at the US ambassador's residence, Mr Trump said: "I think that is very insulting to a lot of different forces.
"It is a very, very nasty statement. I think they have a very high unemployment rate in France. France is not doing well economically at all.
"It is a very tough statement to make when you have such difficulty in France, when you look at what is going on with the yellow vests.
"They have had a very rough year. You just can't go around making statements like that about Nato. It is very disrespectful."