Rishi Sunak awkwardly laughed when he was challenged about the state of the health service by a former NHS worker in Winchester.
The prime minister was walking through the city in Hampshire when he was stopped by a woman who indicated she had worked for the NHS in the past.
In the footage, captured by Sky News, the ex-health worker passionately asked Mr Sunak why strikes are so prevalent, and why he can't make the NHS "all go back to how it used to be".
In a somewhat awkward encounter, Mr Sunak then laughs - as do some of the people gathered around them.
The woman continues "not literally, but if you had a problem you could go to the hospital".
The prime minister then begins walking, joined by the woman, who goes on to plead with him not to close her local A&E department at Royal Hampshire County Hospital.
In an attempt at reassurance, the prime minister stops again and says that all the NHS strikes (other than the dispute with junior doctors) have been resolved.
The pair then shake hands and the woman says "thank you", but not before making one final plea to Mr Sunak.
"Please don't send the A&E to Basingstoke," she says, explaining that her daughter had "spent seven hours waiting" for medical treatment.
The department at Royal Hampshire County Hospital is due to be closed as part of the restructuring of hospitals in Hampshire. Under the plans, a new acute specialist hospital will be built in north Hampshire.
Labour leader Sir Keir Starmer said the moment "reinforces what people think" about the government.
Sir Keir said: "The prime minister doesn't understand what people are going through…. We engage with our plan - we don't laugh and walk away."
Wes Streeting, the shadow health secretary, added that Mr Sunak "has no idea of the misery NHS patients are going through".
Mr Sunak had earlier visited the Silverlake Stadium in Eastleigh, where he said there is "more to come" in terms of tax cuts.
The prime minister said he wanted to slash taxes "when we can responsibly do so", echoing comments made by the chancellor in a fresh hint the Tories could offer a pre-election giveaway.
Talking to Sky News on the fringes of the World Economic Forum in Davos, Jeremy Hunt said on Thursday that "the direction of travel" was for the UK to emulate successful low-tax economies.
Mr Sunak, speaking to broadcasters during a visit to Hampshire, said the 2p cut to the main rate of national insurance that came into force this month had already been a "tax cut for 27 million people in work".
He continued: "And we said that we do want to cut taxes for future events when we can responsibly do so.
"Our priorities are very clear. It is controlling spending and welfare so that we can cut people's taxes."