Culture Secretary Fiona Hyslop has outlined the Scottish government's proposals for a new federal BBC at a meeting with the corporation's head.
Ms Hyslop spoke to Tony Hall about the SNP's wishes to see the BBC operate under a new federal structure.
The party is also calling for the creation of new TV and radio channels for Scotland.
A BBC spokesman said it recognised that there was audience demand for "greater representation".
The next charter will form the basis for BBC operations over the next decade.
Ms Hyslop said: "Scotland has the right to expect something truly radical from the BBC charter review if the organisation is to meet the needs of audiences or support the development of a sustainable production sector in Scotland.
"To reiterate, we're calling for a federal BBC, with at least a board for each nation that should comprise a mix of BBC staff and independent members."
She said budgets should be transferred to BBC Scotland, which would allow independent decision-making, in relation to commissioning and editorial decisions, staffing structures and the wider running of the organisation.
"We're also calling for the creation of a new TV and radio channel to support the demands of audiences and the TV sector in Scotland," she said.
"These proposals must be supported by a proportionate share of the BBC licence fee, addressing the current mismatch between the £335m income for the BBC from Scotland and the £190m spent here, of which only around £35m is spent on TV production for Scotland.
"From the discussions we have held so far with the sector in Scotland, we know there is support for our proposals and an appetite for positive change through the charter renewal process."
The plans were first revealed by First Minister Nicola Sturgeon in August.
The Scottish government now has a formal role in the charter renewal process for the BBC and is consulting relevant people and organisations on its plans.
A BBC spokesman said: "Audiences across Scotland get great value from the licence fee, and are some of the highest users of BBC services. We already spend around £200m per year directly in Scotland, and on top of that audiences get access to UK-wide TV, radio and online programmes and services which accounts for the great majority of use of the BBC by Scottish licence fee payers.
"We recognise that there is audience demand for greater representation and portrayal of Scottish audiences on all BBC services and set out our ambition to achieve this in our proposals for the BBC in the year ahead, including improved news, education and online services.
"The BBC's funding has now been set for the next five years and this will mean cuts across the BBC - we will have to balance our investment on pan-UK services with dedicated services in the nations. We will aim to protect spending in the nations so that content investment is cut less than in other parts of the BBC.
"We look forward to working with the Scottish government on these issues."
Scottish Liberal Democrat leader Willie Rennie said: "The BBC is trusted across the world for the quality of its broadcasting. The SNP don't want to reform the BBC. They want to control the BBC.
"The SNP want the lights turned off on their domestic record. That is what their war on the BBC is all about. They need to stop obsessing over what is happening at BBC Scotland and start focusing on delivering for our schools and hospitals."