Australia's last Liberal government, which was already in minority, is in further chaos after senior MP Elise Archer was sacked as attorney-general on Friday.
Ms Archer subsequently announced she was quitting parliament but has since said she is reconsidering and may remain as an independent.
She has flagged possibly supporting a no-confidence vote in the government in parliament, which is next scheduled to sit on October 17.
If Ms Archer sits as an independent, the government would hold just 10 of 25 seats in the lower house.
Premier Jeremy Rockliff gave a firm ultimatum on Tuesday after the swearing in of his new cabinet.
"I want to be clear, the only way parliament resumes is if Ms Archer resigns as she initially committed, or she provides a written guarantee of confidence and supply," he said in a statement.
"We will not be returning to parliament unless either of these two actions occurs.
"All Tasmanians deserve certainty about the future of their government as soon as possible."
Mr Rockliff asked Ms Archer to resign from cabinet on Friday after workplace bullying allegations against her and messages critical of her colleagues, including Mr Rockliff, were made public.
Mr Rockliff said he had other information about inappropriate messages which prompted his decision.
A message sent by Ms Archer, in which she said she was "sick" of victim-survivors of abuse, was leaked on the weekend.
Ms Archer has denied the bullying allegations and says the victim-survivor message was taken out of context.
Mr Rockliff on Tuesday said he first became aware of bullying allegations against Ms Archer on September 1.
It is understood an allegation was in the process of being investigated when they were made public in an article in The Australian newspaper on Friday.
Tasmania's government has been in minority since May, when two MPs quit to the cross bench over concerns about the state's deal for an AFL team and stadium.
As part of the government's ministerial reshuffle, Health Minister Guy Barnett was appointed new attorney-general.
If Ms Archer leaves parliament it will prompt a recount in her seat of Clark, which is likely to be won by a Liberal.
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