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 detail about the matter, describing it as a "complex matter", but disclosed taxpayers spent about $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 fees.
In a letter to the premier, they have demanded answers to 20 questions and have threatened further action if a response isn't provided by Friday.
"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 options include referring the premier to parliamentary committees for interrogation or a censure motion.
Tasmania's Labor opposition has also questioned the premier but ruled out moving a no-confidence motion.
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.
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.
Independent David O'Byrne stopped short of signing the letter but said he shared concerns about the premier's conduct.
Transport and Infrastructure Minister Kerry Vincent said the government wasn't stonewalling.
"I have no doubt the premier will make more comments when he is legally able to," he said.
"This is purely about a legal situation that is very complicated."
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."
Labor said it welcomed the letter but wants the scrutiny widened to include Racing Minister Jane Howlett, who has spent $300,000 of public money on legal fees since 2023 in the course of ministerial duties.
The government has said Ms Howlett's fees were paid in line with indemnity protocols.
