"Given any significance of any decisions, which may have seen me become an independent member of the Parliament, leaving the government in minority, I believed it was important to enter into further urgent discussions with the Premier prior to making a final decision," Ms Hickey said in a statement on Friday.

Ms Hickey said Premier Will Hodgman's willingness to address with priority issues including homelessness, health, mental health and general matters of social disadvantage was the reason she chose to remain in the party.

MORE ON SUE HICKEY'S TIME AS SPEAKER:

"The Premier understands my position and has shown strong leadership in seeking to address my concerns," Ms Hickey said.

"For these reasons I intend to remain a member of the Tasmanian Liberal Party and part of the majority Hodgman government."

To remain with the Liberals, Ms Hickey said she secured a state of the art drug and rehabilitation centre for the state's south.

"Today the Premier and I have committed to working with the Minister for Mental Health Jeremy Rockliff to deliver at St Johns Park a state of the art Drug and Alcohol Rehabilitation centre," she said.

"My vision is for a 50-bed facility including step down units and 10 of these beds would be devoted to adolescent for mental health conditions.

"It was agreed that work would be commenced immediately on this proposal with a view to completing the project as soon as possible."

Ms Hickey said health remained a concern.

"I remain particularly concerned about the Royal Hobart Hospital, the Launceston General Hospital, the very poor state of our ambulance vehicles, and the lack of staff. I believe these issues are also of fundamental concern to the wider Tasmanian community."

The Speaker issued a threat to depart the government on Sunday after she was left incensed when Mr Hodgman did not consult with her about a cabinet reshuffle announced over the weekend.

She was also overlooked a second time for a cabinet position which she said was promised to her if she ran for the Liberals in the 2018 state election.

Ms Hickey retaliated last year by accepting a nomination from Labor, supported by the Greens, to take the Speaker's chair over the government's choice of former parliamentarian Rene Hidding.

Since then, she has used the position to force the government to provide additional money for women's health services, criticised its performance on actions in the health and housing portfolios, and voted against the government a number of times.

Her vote was crucial for changes made to the way gender would be recorded on birth certificates and how Tasmanians would be able to change their gender in the future.

Earlier on Friday, new Health Minister Sarah Courtney said Ms Hickey had provided a commitment to the government in regards to supply and confidence and the Speaker's announcement was a matter for her.

Ms Courtney reiterated that she was part of a strong, stable united Liberal team.

Prior to the 2018 state election, the Premier said he would not govern in minority.

When asked if Mr Hodgman would have to resign if Ms Hickey left the party, Ms Courtney said she had "every confidence Will Hodgman will continue as leader of our party."

Greens leader Cassy O'Connor said she would work with Ms Hickey whether she was a member of the Liberal party or an independent.

"Sue and I have a good relationship. I am often entertained by her, often mystified," Ms O'Connor said.

Ms O'Connor said Ms Hickey's decision to stay in the Liberal party would be an interesting test for the Speaker.

"People will scratch their heads a bit, given the level of discontent and the things she has said about her colleagues," she said.