The Prime Minister hit out at the broadcaster's plan to restrict the benefit to just the poorest pensioners.
Speaking to reporters at the G7 summit in Biarritz he said: "The BBC received a settlement that was conditional upon their paying for TV licences for the over-75s.
"They should cough up."
The Tory election manifesto in 2017 pledged to protect free licences.
But the benefit will be restricted to those on pension credit from June next year, with the BBC saying it cannot afford to take on the financial burden from the Government.
The move will strip 3.7 million pensioners of their free licence.
The free TV licence was introduced in 2000, but the BBC agreed to take on the cost as part of the charter agreement hammered out in 2015.
Those found to be ineligible for a free licence will have to pay £154.50 a year for a colour television and £52 a year for a black and white television.
A BBC spokeswoman 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.
"If the BBC funded all TV licences for the over-75s it would mean the closure of BBC Two, BBC Four, the BBC News Channel, the BBC Scotland channel, Radio 5 Live, and several local radio stations.
"It is a matter for the Government if it wishes to restore funding for free licences for all over-75s."
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.
"Keeping the free licences was a Tory manifesto promise, but because of this Government's refusal to fund the concession, millions of older people will have their free TV licences scrapped next year.
"This Government must stop passing the buck and step in to fund the free TV licences today."
A Number 10 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."