Premier Jeremy Rockliff has faced sustained questioning after party colleague Madeleine Ogilvie quit her ministerial roles on May 30 following allegations she misled state parliament.
Ms Ogilvie told a parliamentary hearing in 2025 she had not been involved in any Supreme Court action in the past 18 months.
But in May she revealed she had been a party to Supreme Court proceedings she had initiated.
The government has provided scant details about the matter, describing it as a "complex matter", but disclosed taxpayers spent around $120,000 on Ms Ogilvie's legal fees between 2023 and 2025.
The Greens and independents Kristie Johnston, Peter George and Helen Burnet have said Mr Rockliff has refused to answer straightforward questions about the matter.
In a letter to the premier, they demand answers to 20 questions and have threatened further action if a response isn't provided by Friday.
The move comes after the island state was flung into an early election in mid-2025 when Mr Rockliff lost a no-confidence motion critical of his budget management.
Tasmania's Labor opposition, who have also questioned the premier, have ruled out moving a no-confidence motion.
Among their questions, the letter's seven signatories want answers about when Mr Rockliff became aware Ms Ogilvie was involved in a Supreme Court case.
They also want to know when he became aware her answers to a parliamentary committee were potentially misleading.
"We reserve the right to use the parliamentary options available to us to pursue the required accountability owed to Tasmanians," the letter, released on Monday, says.
"The outcome we seek is a functional parliament that is focused on Tasmanians' best interests," they say.
"Central to this is integrity and accountability. We trust you share these priorities."
At a budget estimates hearing on June 1, Mr Rockliff said Ms Ogilvie's legal funding was within guidelines.
"These are complex matters and I'm not going to be commenting any further ... especially given the confidentiality requirements," he said.
"Ms Ogilvie has given an undertaking as other members have to provide full details when Ms Ogilvie is legally entitled to."
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