But the prime minister was accused of an “appalling” disregard of pensioners for seeking to offload blame for the decision to means-test the subsidy on to the broadcaster.
And the BBC said that funding free licences after 2020 – when the government will stop providing financial support for the scheme – would mean closing down services including BBC2, BBC4, the BBC News channel, BBC Scotland, 5 Live and local radio stations.
The Conservative manifesto for the 2017 general election included a pledge to preserve the free licence at least until the end of the parliament, due in 2022.
But responsibility for deciding whether to continue with the scheme was handed over to the BBC as part of a 2015 settlement, which required the broadcaster to shoulder the cost of free licences, previously covered by the government.
The BBC announced earlier this year that it would means-test the licence from next June, meaning 3 million households will have to start paying the £154.50 annual fee.
Asked whether he planned to honour his party’s manifesto pledge, Mr Johnson replied: “The BBC received a settlement that was conditional upon their paying for TV licences for the over-75s. They should cough up.”
A BBC spokesperson said: “It was the government who decided to stop funding free TV licences for the over-75s, and parliament gave responsibility to the BBC to make a decision on the future of the scheme.
“There was no guarantee that the BBC would continue to fund free licences for the over-75s, as the culture secretary at the time has confirmed.
“We’ve reached the fairest decision we can in funding free TV licences for the poorest pensioners, while protecting BBC services.
“It is a matter for the government if it wishes to restore funding for free licences for all over 75s.”
Labour’s shadow culture secretary, Tom Watson, said: “This prime minister’s disregard for older people is appalling.
“He is trying to blame the BBC for his own government’s policy, but this obfuscation will not work.
“The blame for scrapping free TV licences lies firmly with the government.
“This government must stop passing the buck and step in to fund the free TV licences today.”
But a Downing Street source said: “The government agreed the licence fee settlement with the BBC in 2015. At the time, the director general said it was a ‘strong deal for the BBC’ and provided ‘financial stability’.
“It saw BBC income boosted by requiring iPlayer users to have a licence, and unfroze the licence fee for the first time since 2010 – with it rising each year with inflation.
“In return, we agreed responsibility for the over-75 concession would transfer to the BBC in June 2020. The BBC must honour this agreement.”
The head of the Broadcasting, Entertainment, Communications and Theatre Union, Philippa Childs, said: “It’s very disappointing that Boris Johnson continues with the narrative that the BBC knew what they were taking on.
“The reality is that they were given little or no choice at the time, when austerity was at its peak and ministers were looking for a convenient way to pass the buck on taking difficult decisions about welfare payments.”
Ms Childs warned that continued funding of the subsidy would mean cuts of a size which cannot be achieved without “significantly impacting the quality of the BBC’s output”.
“This would be incredibly self-defeating for the public service broadcaster which remains the envy of the world,” she said.
But the political director of the TaxPayers’ Alliance, which lobbies for lower taxes, said Mr Johnson was “tuning into the public mood”.
James Roberts said: “The Beeb should be moving towards a funding model where subscription fees replace part or all of the licence fee, so that we can just axe the TV tax and only those who watch it need to pay.”