The clear winners in Saturday's state election were the Greens, who now hold the balance of power in a hung parliament.

But it will be either Liberal leader Will Hodgman or the Labor incumbent David Bartlett who will go to the Council of Australian Governments, which has been pushed back a week to April 19.

Two state seats remain in doubt, and it could take weeks before they are decided.

Yesterday, Greens leader Nick McKim didn't have a plan in mind about what role his party might have in trying to influence which of the two major party leaders attends COAG.

Mr McKim was asked by a reporter in Hobart whether he would seek to talk to whoever was the new premier before COAG and have the Greens' interests represented at the meeting.

''That depends on what happens over the next few days and next couple of weeks and I'm not in position to predict that at the moment,'' he said.

Mr McKim was specific about the Greens' concerns about Prime Minister Kevin Rudd's plan. ''We need to see more detail around whether there will be job losses in the public sector, particularly amongst health workers,'' he said.

The outcome of Saturday's poll is an expected 10-10-5 split of Liberal, Labor and Greens in the 25-member Assembly.

The Greens are still in the race to gain one more seat, that of Denison in Hobart, which would take them from four to six seats, assuming they hold on to their likely gain in the north-west seat of Braddon. The man expected to become Tasmania's next premier, Mr Hodgman, says he'll act in the state's best interest on the Federal Government's planned funding takeover of hospitals.

Issues such as reduced GST revenues and the prospect of hospital closures in regional and rural centres were chief among his concerns about the plan.

''These things are very important here in Tasmania,'' he said yesterday.

Mr Bartlett supports the takeover and had hitched most of Labor's central health policy platform to it in his election campaign.

The incumbent Premier said it would be days before he knew whether he had lost office.

''Anything can happen in a couple of electorates, for those fifth seats, and we'll wait patiently,'' he said.

On Saturday, Mr Hodgman laid claim to being the premier of the state's hung parliament after Labor suffered a general 12 per cent swing against it.

The Liberals have polled more votes overall than Labor and in the event of a tie it has been agreed he would become premier.

AAP