The end of the licence fee has been mooted by the UK Government, with a threat to turn the BBC into a subscription service.
It was later said, by a Downing Street spokesman, that Prime Minister Boris Johnson does not want to scrap “all licence fees” at this stage.
Director-general Lord Hall hit back at a suggestion the BBC was redundant following the rise of streaming services such as Netflix and Amazon.
The licence fee model means “You’ve got to give something to everybody – I think that is a fantastic creative challenge”, he told a conference.
“I hope we are developing and continuing to develop a much warmer relationship with the British public, which is less the ‘Auntie’ of two or three decades ago and much more something which is interwoven in people’s lives. We are there in people’s lives.”
Lord Hall went on: “People say things like, ‘What’s the point of the BBC when you’ve got the streamers?’
“The BBC is not Netflix, it really isn’t ... Netflix don’t do sport, they don’t do news, they don’t do a whole raft of things.”
Lord Hall added: “It’s really important ... to see what the BBC does in the round.
“The licence fee, I think, beyond 2027 [when the BBC’s charter comes up for renewal] will still matter and will still be phenomenally important for the BBC.”
The broadcaster, which celebrates its centenary in 2022, is believed to have got its “Auntie” nickname because of an “Auntie knows best” image in previous decades.
The UK Government was yesterday accused in the Lords of “intimidation and destabilisation” towards the BBC.
Film producer Lord Puttnam warned that an “unremitting vendetta” must not be allowed to rob the nation of such a valuable asset.
The Labour peer said: “The current project to undermine public service broadcasting is not new.”
It was part of a “decades long campaign of salami-slicing and intimidation by successive Conservative governments”, he said.
Tory administrations had sought to “take the wind out of the BBC’s sails and erode the trust it enjoys from the public”.
Lord Puttnam said the Conservative Party should be proud of the BBC rather than trying to dismantle it.
Lord Hall said the BBC had “constantly reformed itself” from radio to television, and 24-hour news to online.