Jeremy Rockliff faces becoming the first Tasmanian premier to be censured by parliament after the resignation of two ministers over transparency concerns.
Liberal MP Madeleine Ogilvie moved to the back bench on May 30 and colleague Jane Howlett on Tuesday amid accusations they misled parliament and questions about spending of taxpayer funds on "secret" court cases.
Ms Howlett has spent $405,000 of public money on legal fees and Ms Ogilvie $120,000, but details about the matters have not been disclosed by the government.
Mr Rockliff on Wednesday told parliament both sets of spending appeared "on face value" to be related to Integrity Commission investigations.
Greens leader Rosalie Woodruff moved a censure motion against Mr Rockliff, who governs in minority, on Wednesday.
