Digital TV channels BBC Three and Four are safe from the axe "at the moment", the corporation's chairman has said.
With budget cuts on the way, there have been calls to close a channel in order to safeguard quality in other areas.
But Sir Michael Lyons, who chairs the BBC Trust, said shutting channels would mean "retreating from audiences".
He was talking to BBC Radio 4's Today host John Humphrys, who recently said he was "massively concerned" at the prospect of cuts to his programme.
Humphrys has said digital channels should be scrapped instead of making "damaging cuts to core programmes".
He told Sir Michael that Radio 4 cost 16 times less than BBC Three, based on the cost per user per hour.
"Could you not argue that the public has already decided that they want one service rather more than they want another service, and therefore that that one service deserves more money than the other?" he asked.
Sir Michael said BBC Three and Four were "very focused" on specific audiences.
"BBC Three is targeted at young people, which we know to be an audience the BBC doesn't adequately cover, and BBC Four tries to capture what we might call the best-informed viewers," he said.
"This is part of the BBC's ambition to touch every part of the audience, to offer something special to every single licence fee payer.
"It mustn't back off from that, otherwise I think it puts in jeopardy the very nature of its role in this country."
'Distinctive' programmes
Humphrys, however, said it was a "fundamental fallacy" that the corporation could cater for everybody.
Sir Michael replied: "At the moment, our judgement is that it would not be right to shut down any of our channels or stations. At the moment."
He added that the BBC's TV offering could be reassessed once the digital switchover is completed in 2012, "but it would mean retreating from audiences and going backwards on the clearly experimental channels that were set up".
The corporation, he said, would have to make less content - but make sure the programmes it did make were "truly distinctive".
Jeremy Paxman has also voiced his fears about cut-backs, saying Newsnight could not "survive in anything like its current form" if its budget was slashed by 20%.
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