UK Health Secretary Jeremy Hunt immediately retaliated with a defence of the British healthcare system, saying it was preferable to that in the US.
Later the Prime Minister’s official spokesman also hit back at Trump’s remarks.
He said: “The Prime Minister is proud of having an NHS that is free at the point of delivery.
“NHS funding is at a record high and was prioritised in the Budget with an extra £2.8bn.
“In the recent Commonwealth Fund international survey, the NHS was rated the best in the world for a second time.”
The spokesman insisted May enjoys a “good relationship” with the president, but his latest remarks will put further strain on the special relationship.
In November, Trump retweeted three videos about Muslims depicting them as dangerous - with commentary that was heavily debunked - from Jayda Fransen, deputy leader of the fringe far right group Britain First.
In response, May said: “It is wrong for the president to have done this.” She added Britain First “cause anxiety to law-abiding people.
“British people overwhelmingly reject the prejudiced rhetoric of the far-right which is the antithesis of the values that this country represents: decency, tolerance and respect.”
The Prime Minister has also had to counter Trump when he tweeted about the Parsons Green attack in London and after he signed an executive order banning travel to the US by citizens of seven Muslim countries.
Two weeks ago, the pair had apparently settled their differences at the World Economic Forum in Davos.
The US President referenced a protest outside Downing Street at the weekend in which thousands of people called for more money to be given to the health service.
Crowds chanted slogans including “saving lives costs money, saving money costs lives” and “keep your hands off our NHS”.
Many on the the left in the US want to see system of single-payer or state-funded universal healthcare replace a system dominated by private sector providers and insurers.
Trump’s comments were raised during an urgent question in the House of Commons.
Labour’s Shadow Health Secretary Jonathan Ashworth, said: “On Saturday, thousands of us took to the streets to demand a fully funded, universal public National Health Service.
“And, by the way, we will take no lessons from Donald Trump who wants to deny healthcare to millions with a system that checks your purse before it checks your pulse.
“The NHS model isn’t broke, but it does need funding. If this government doesn’t give it the funding it needs then the next Labour government will.”