Sir Michael Lyons said the findings will be put to the Government
About half of licence fee payers would want the charge to be smaller if given the option, an independent poll commissioned by the BBC Trust found.
Since 2007, £5.50 of the fee has been used to pay for the digital switchover.
The poll of 2,068 people found most want it cut by that amount after 2012 - when switchover ends - and most do not want the money to go to other channels.
A government spokesman said: "Without action, we risk losing regional news anywhere except on the BBC."
Meanwhile, the trust has announced a full-scale review of which activities the BBC should focus on in the future.
The review will be conducted by BBC director general Mark Thompson.
Trust chairman Sir Michael Lyons said the corporation needed to "focus on what makes it different and distinctive from commercial media" and to "make sure it doesn't ask the public for more money than it needs to do its job".
The BBC would have to "think bigger, even though it may mean the BBC becoming smaller," he added.
Sir Michael's comments came in an unprecedented open letter to audiences, in which he released the findings of the Ipsos Mori poll, which surveyed 2,068 adults about the future of the licence fee.
He said the results reinforced the trust's "concern about any attempt to use the licence fee to subsidise commercial operators, as proposed by the government in its Digital Britain report".
He added that he now had a "clear message" from the public, which will be put to the government.
Both Sir Michael and Mr Thompson have previously spoken out against government proposals to "top slice" £130m from the annual licence fee to be used as a fund for regional news on ITV and children's programmes.
However, although most people surveyed said they wanted the licence fee to be kept within the corporation, only 17% said the £5.50 digital switchover fee should be absorbed into BBC programme-making budgets after 2012.
The BBC Trust's poll comes days after a separate survey for the Guardian newspaper suggested that four out of five people thought the UK should be proud of the BBC.
Mr Thompson said: "None of this comes as a surprise to us - our own tracking research has indicated that, at a time when public faith in many other British institutions is eroding fast, belief in the BBC is actually strengthening."
But a spokesman for the Department of Culture, Media and Sport said that action was needed to protect regional news output.
"Numerous surveys have shown the public value local and regional news, and the BBC survey shows that people are not opposed to the principle of the licence fee being shared." he added.
"We have been very clear that if the BBC, or anyone else, has a better idea as to how to safeguard its future we are keen to hear it."