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.
He could become the first premier in Tasmania's history to cop a censure, which is a rebuke from parliament but doesn't carry any penalty.
The motion accuses Mr Rockliff of failing to uphold the ministerial code of conduct in relation to Ms Ogilvie and Ms Howlett.
Mr Rockliff also failed to ensure Ms Ogilvie corrected the record when he became aware she misled parliament and failed to answer questions about the matter, the motion says.
"This is a very grave situation the premier has brought himself to," Dr Woodruff said.
"We're now in a position where doubt is cast on every word out of the premier's mouth."
Treasurer Eric Abetz said the issues raised in the motion had been dealt with following Ms Howlett and Ms Ogilvie's resignation from cabinet.
"We on this side will defend the premier's integrity and reject the assertion of the leader of the Greens," he said.
Labor's Ella Haddad said the "caravan hadn't moved on" and there were still questions to be answered by the premier and the government.
Debate on the motion will continue on Wednesday.
Mr Rockliff lost the confidence of parliament in 2025 over his management of the budget, prompting a snap election that returned another hung parliament.
Ms Ogilvie in November told a parliamentary committee she wasn't a part of any legal action, before later admitting she had initiated a Supreme Court matter.
Mr Rockliff has apologised over his handling of Ms Ogilvie's scenario and said he should have interrogated her answers more thoroughly.
Ms Howlett resigned after evidence was heard at a committee that her office was aware of campaign texts sent in breach of conventions, when she had previously claimed no knowledge.
Mr Rockliff has said details about Ms Ogilvie and Ms Howlett's legal matters will be made public when they legally can.
The approval of taxpayer funds for legal costs was done within the guidelines, the premier has said.
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