Boris Johnson has raised the possibility of scrapping the TV licence fee by admitting he is "certainly looking at" the issue.
As he continued campaigning in the North East ahead of Thursday's general election, the prime minister questioned "how long" the current system of funding the BBC can be justified.
He also claimed the BBC should "cough up" and fund free TV licences for over-75s.
But Mr Johnson stressed he was keen not to create policy "on the hoof" in the last few days of the election campaign.
Labour immediately accused the prime minister of a "pathetic attempt" to distract from questions about the NHS.
The prime minister was also quizzed on Monday about the Daily Mirror's publication of a picture of a poorly four-year-old boy, who the newspaper reported was forced to sleep on a hospital floor for more than four hours because of a shortage of beds.
Asked by a worker at Fergusons Transport, near Washington, whether he would abolish TV licence fees, the prime minister replied: "For everybody?
"Well, I don't think at this late stage in the campaign I'm going to make an unfunded spending commitment like that.
"But what I certainly think is that the BBC should cough up and pay for the licences for the over-75s as they promised to do.
"But at this stage we are not planning to get rid of all TV licence fees, though I am certainly looking at it."
A TV licence currently costs £154.50 per year for a colour TV and £52 for a black and white TV set.
It is a criminal offence to watch live TV without a valid licence.
The BBC agreed to take on responsibility for free TV licences for over-75s from the government - estimated to cost around £700m per year - in 2015, following a negotiation with ministers over the corporation's financing.
However, in June, the BBC controversially announced a free TV licence will only be available to households with someone over 75 who receives pension credit from next summer.
About 3.7 million households which previously received a free licence will have to pay for one under the new scheme.
In October, Culture Secretary Nicky Morgan told a committee of MPs she is "open-minded" about scrapping the licence fee and replacing it with a subscription service for BBC channels, such as the model used by Netflix or Sky.
Mr Johnson also hinted at rethinking how the BBC is funded, despite confessing to Fergusons Transport workers he is "under pressure not to extemporise policy on the hoof.
He added: "You have to ask yourself whether that kind of approach to funding a TV, a media organisation, still makes sense in the long-term given the way other organisations manage to fund themselves - that's all I will say.
"I think that the system of funding by what is effectively a general tax, isn't it, everybody has a TV, it bears reflection - let me put it that way.
"How long can you justify a system whereby everybody who has a TV has to pay to fund a particular set of TV and radio channels? That is the question."
The Conservatives' election manifesto makes no mention of scrapping the TV licence fee, but states the party believes free TV licences for over-75s "should be funded by the BBC".
Labour's manifesto says they will "protect free TV licences for over-75s".
Responding to the prime minister's remarks, Labour's shadow culture secretary Tom Watson said: "This is a pathetic attempt by Boris Johnson to distract from his refusal to even look at the picture of a four-year-old boy forced to sleep on a hospital floor.
"We already know that Boris Johnson is a danger to our NHS.
"His comments today reveal that he will threaten the very existence of another of Britain's great institutions, the BBC, by scrapping its funding mechanism."