Ms Archer was punted from cabinet by Premier Jeremy Rockliff over allegations of workplace bullying and text messages he deemed inappropriate.

On Wednesday morning, Mr Rockliff set Ms Archer a deadline to either leave parliament or confirm she would back his government as an independent.

The premier said he would call an early election if she didn't meet the deadline.

A few hours later, Ms Archer announced her resignation, accusing Mr Rockliff of denying her due process.

"This is done with an extremely heavy heart particularly given the outpouring of support I have received, encouraging me to stay on," she said.

"However, this is the right decision for me personally, knowing the types of threats and tactics adopted by this government recently are likely to continue."

Ms Archer, who previously said she may stay in parliament as an independent, said she would not have been able to provide the premier or the government with confidence.

In a 900-word statement she described Mr Rockliff's ultimatum as aggressive and erroneous, saying the terms were "blatantly incorrect".

"I always intended to make my decision about whether to resign from parliament as quickly as possible in the interests of Tasmanians," Ms Archer said.

"But intense media interest and now this threatening behaviour from the premier and (his) office over a longer period have unduly pressured my decision."

In messages leaked last week and at the weekend, Ms Archer described Mr Rockliff as "too gutless" to be leader.

In another, she said she was "sick" of child sexual abuse victim-survivors, which she claimed was taken out of context.

She has also denied the bullying allegations.

"The premier had still not afforded me any due process, which was palpably unfair, and had not provided any factual particulars of the disputed claims against me," Ms Archer said.

Mr Rockliff said Ms Archer's decision to resign was the right thing to do.

"If culture is to change in this state it requires leadership and accountability, starting at the top - no matter how challenging the consequence of those decisions might be," he said.

"I am hopeful the events of the past few days open a new chapter in standards and accountability in Tasmania."

Ms Archer, who was Tasmania's first female Speaker, blamed the leaking of the messages on the premier's office through "third parties".

Mr Rockliff has denied he or his office leaked the texts.

"He is big on tough talk in the media but has not contacted me personally for my support," Ms Archer said.

"This is entirely consistent with his leadership style and has also contributed to the loss of other members."

Tasmania's Liberal government has been in minority since May, when two MPs left the party to sit as independents due to concerns about the state's AFL deal and Hobart stadium plan.

Ms Archer's decision to quit parliament will prompt a recount in her seat of Clark, which is likely to be won by a Liberal.

The government held 11 of 25 lower-house seats before Ms Archer's resignation.

Mr Rockliff has confirmed parliament will return as scheduled on October 17 and he will take up the Labor opposition's offer of a 'pair'.

Australian Associated Press