He said the federal government will reduce its income tax by an agreed percentage and allow state governments to levy an income tax equal to that amount.
"There would be no increase in income tax from a taxpayers' point of view - he or she would pay the same amount of income tax, but the states would be raising the money themselves," Mr Turnbull told reporters in Sydney on Wednesday.
Mr Turnbull said the biggest change to income tax powers since World War II is in recognition that there is a failure at the heart of the federation.
"It is the failure of the states to have access to the revenue sources," he said.
States that needed more funding for a service such as health would go to their parliament and raise the money, then go to the people and persuade them of the merits of it.
"This is a real opportunity to make the federation work," Mr Turnbull said.
He said the proposal had been put forward to premiers, chief ministers and their senior officials ahead of Friday's Council of Australian Governments meeting.
Earlier, Treasurer Scott Morrison said states and territories need to be more accountable when it comes to paying for the services they deliver.
But he stopped short of confirming a proposal that they be allowed to raise income tax to fund hospitals and schools.
"You have a situation where you have one level of government which is running programs and controlling, or not controlling, costs and you've got another level of government which is increasingly having to foot the bill," Mr Morrison told reporters in Sydney on Wednesday.
"It is a very good business practice that those who fund something are also the same people who control the cost of how it's being delivered."
Cabinet minister Darren Chester says it's an economic reform well worth pursuing.
He said clearer lines of responsibility between states and the Commonwealth are needed to end blame shifting, frustration and duplication of services.
But Labor frontbencher Ed Husic says it'll create a double taxation mess.
"Tony Abbott even said he did not want to touch double taxation and go back to the 1940s," Mr Husic said.
State premiers and territory chief ministers are expected to be briefed on the plan when they meet in Canberra this week, as part of the federal government's proposal to fix a looming hospital funding black hole.
