Liberal leader Jeremy Rockliff is courting crossbench members to form a minority government after being unable to secure the 18 seats required for majority in Saturday's election.
The Liberals appear on track to secure 15 seats, with the final make-up of the state's lower house not likely to be known for weeks.
Labor, which has been in opposition since 2014, on Sunday conceded they were unable to form a minority government with just 10 seats to their name.
The Jacqui Lambie Network has two seats and will likely win a third, with their successful candidates to be known once counting continues in earnest after Easter.
Two independents, left-leaning Kristie Johnston and former Labor leader David O'Byrne, have also been elected.
The proposed $715 million stadium at Macquarie Point in Hobart was a major election issue. (HANDOUT/AFL)
Mr Rockliff told reporters on Thursday he was looking forward to discussions with the group continuing.
"I'm very confident our crossbenchers, our independents … want to see a very good parliament," he said.
"A parliament that works together, a parliament that provides Tasmanians with certainty and stability."
Liberal-backed plans for a $715 million stadium at Macquarie Point in Hobart, a condition of the state's licence for an AFL team, was a big election issue.
Former Labor leader Rebecca White, who stepped down from the role on Tuesday, described the stadium as a bad idea and campaigned on trying to renegotiate the deal.
The Greens, who have four seats and could secure more, want to kill off the stadium.
Jacqui Lambie Network candidates are on both sides of the fence, while Ms Johnston is against and Mr O'Byrne is starting from a position of 'yes'.
The project will be assessed by the state's planning commission and then must be voted through both houses of parliament to get the green light.
The planned stadium is a condition of the state's licence for an AFL team. (Loic Le Guilly/AAP PHOTOS)
Mr Rockliff said he was confident the stadium would proceed.
"We will push ahead. It is in the planning system and there is a lot to work through," he said.
"My view is we can work through the stadium with the new parliament. I'm very excited about that opportunity.
"People knew where I stood, many Tasmanians probably disagreed. But at least they knew where I stood and where I stand."
Tasmania's AFL club, which was officially launched during the final week of the election campaign, has attracted more than 150,000 foundation members.
The AFL has been unmoved in its position that the stadium contract must be honoured.
SEATS IN TASMANIA'S NEW PARLIAMENT
* Liberal 12, Labor 10, Greens four, Jacqui Lambie Network two, independents two, in doubt four.
11°C