He added that he was a " supporter of the licence fee", but argued that, with declines in revenues for channels funded by advertising and subscriptions, it was important to avoid creating a system which was "not in balance".
He said: "The BBC is an important national institution. I want to see it prosper and succeed and be a fantastic cultural asset."
Culture Secretary Andy Burnham said Mr Cameron was "planning for today's headlines instead of the future of the BBC".
He said that if he "really wants to help families he should back our cut of £5 a week off the average household VAT bill" rather than using the BBC as a "political football in this way".
Liberal Democrat culture spokesman Don Foster said: "It's a sad reflection of the Tory party that the best it has to offer taxpayers in the economic downturn is £3 off their licence fee.
"With many viewers staying at home a lot more during the recession, it really doesn't seem the right time to be cutting the quality of our television programmes."
BBC Trust chairman Sir Michael Lyons told BBC Radio 4's PM programme: "On the face of it, it [Mr Cameron's call] seems a fairly modest proposal.
"What it would take out of the budget this year is about £80m on a completely unplanned basis."
This was the equivalent of Radio 4's budget for the year, he added.
Sir Michael said the BBC's own planned efficiency savings of 3% a year had been planned so they did "not damage" programmes.
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