Jeremy Rockliff has declared he has a mandate to rule after the Liberals won the most seats at the state election.
Labor counterpart Dean Winter has ruled out doing a deal with the Greens, but wants their confidence and supply votes to govern.
The poll on Saturday was the state's second in as many years and delivered another hung parliament.
With two seats still in doubt, the Liberals have secured 14 and Labor 10 - both short of the 18 needed for a majority - with the Greens on five and four independents.
Several independents have said they are open to backing Mr Rockliff or Mr Winter as premier, but talks are in their infancy.
The final make-up of parliament might not be known until August 2 after the distribution of preferences starts on July 29.
Mr Rockliff on Tuesday said he had presented the four independents, plus Shooters, Fishers and Farmers' Carlo Di Falco, who is likely to get an in-doubt seat, with a draft stability agreement.
The agreement includes setting up a multi-partisan budget panel and for regular cabinet consultation with the cross bench on major policy directions.
There is also a "code of engagement" that says a diversity of views should be recognised as a strength not a weakness.
The agreement would be co-designed with the cross bench, Mr Rockliff said.
"What I want to see is a mature discussion. I believe we can make this parliament work, people expect us to make it work," he told reporters.
Complicating cross bench negotiations is the fact the Liberals and Labor back a new AFL stadium and industrial salmon farming, which the majority of the independents and Greens oppose.
Mr Rockliff and Mr Winter have spruiked a need for collaboration, but have also said they will not back down from the stadium or key policies.
Mr Winter has ruled out "doing a deal" with the Greens, even though Labor requires their numbers to govern.
Greens leader Rosalie Woodruff has urged Mr Winter to pick up the phone so the two parties could talk about an alliance.
Mr Rockliff was in the box seat to form government, political analyst Richard Herr said.
"Both in terms of numbers in the house and with the difficulty for the opposition cobbling together enough from a lower base to actually ... control the house," Professor Herr said.
The Liberals have been in minority since 2023 when two MPs quit the party.
The 2024 poll resulted in a hung parliament, with the Liberals continuing to govern.
A snap election was called in June when Mr Rockliff lost a Labor-led vote of no confidence.
Labor has been in opposition since 2014 and has struggled for traction despite ballooning net debt and infrastructure stuff-ups under the Liberals.
The party has recorded 25.8 per of the primary vote - its lowest in Tasmania in more than a century - despite getting a huge swing in the state at the May federal election.
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