Saturday's snap poll, 16 months after the last, returned another hung parliament with the Liberals securing 14 seats and Labor nine, both short of the 18 needed for majority.
Labor leader Dean Winter, whose party suffered its worst-ever primary vote in Tasmania, says Premier Jeremy Rockliff has "the first opportunity" to form government.
Mr Winter has not closed the door on trying to govern if the Liberals can't, but interestingly, has maintained he won't do a deal with the Greens, whose five votes he needs.
Four independents have been elected, with counting still to decide three seats.
Craig Garland and Kristie Johnston, who both oppose plans for a new $945 million AFL stadium in Hobart, have been returned.
Anti-salmon farm campaigner Peter George, who is also against a stadium, will sit in parliament for the first time, while incumbent stadium supporter David O'Byrne is back in.
Mr Rockliff told reporters on Sunday he had reached out to the cross bench and would ask the governor to re-commission his government.
"My view is the cross bench in the cold, hard light of day will recognise the (Liberal) party ... with the most number of seats (is) able to form a cabinet," he said.
Mr Garland told AAP he was prepared to support Mr Rockliff or Mr Winter as premier and would have further chats once the dust settled.
Ms Johnston had said she would not enter into a formal deal for confidence and supply with either major party and would provide support on merit.
Tasmania is likely to be in political limbo for weeks with the count not expected to be complete until August 2.
Mr Rockliff reiterated he would not back away from his pet-project stadium, a condition of the Tasmania Devils' licence to enter the AFL in 2028, or his support for salmon farming.
Mr Rockliff noted Labor's support for the stadium and the fact two major parties would likely make up 24 or 25 seats in the 35-seat lower house.
"What the vote said is that two-thirds of Tasmanians voted for pro-Tassie Devils and pro-stadium candidates," he said.
Mr Winter said his support for the stadium remained solid after he was asked if he would concede to gain the support of the anti-stadium Greens.
The Tasmania Devils said they were eager to work with an incoming government once the election outcome was finalised.
"We are focused on entering the AFL and AFLW by 2028. In order to do that we have several time frames that must be met," the club said in a statement.
Greens leader Rosalie Woodruff said her party was hopeful of having conversations with Mr Winter but would continue to fight against the stadium.
"We see there are a world of possibilities in the next couple of weeks and that is a fantastic thing for Tasmanians who want a change," she told reporters.
The early election was triggered in June when Mr Rockliff lost a no-confidence motion critical of ballooning debt under the Liberals and bungled Bass Strait ferry delivery.
The motion was supported by Labor, the Greens and three crossbenchers including Mr Garland and Ms Johnston.
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