Opposition health spokeswoman Vicki Dunne tabled the motion in the Assembly, arguing Ms Fitzharris had failed users and employees of Canberra's health system on a raft of matters ranging from bullying and cultural problems to growing waiting lists for surgeries.

Mrs Dunne said the motion was a rebuke of Ms Fitzharris' performance at the territory's health minister, arguing it was unprecedented that the Assembly's standing orders should not be suspended to allow debate on the motion.

She said it was imperative the matter was put to bed one way or another, and for the sake of the Ms Fitzharris, the government address the litany of failures detailed in her motion.

She also argued Ms Fitzharris had failed to address poor management in the ACT Health system, a high churn of staff since the announcement in March of a major restructure, failures in delivering infrastructure at Canberra Hospital and delays to the delivery of a $500 million new building at the hospital promised in 2016.

But Chief Minister Andrew Barr rejected suspending standing orders to allow the motion to be formally debated, saying the Assembly had too much on its agenda to allow a 90-minute debate on the motion.

He said instead, he was happy to allow a debate on the motion on Wednesday, during private members' business day.

Manager of government business Mick Gentleman said the motion was straight out of Tony Abbott's playbook, and with six bills to consider and nine more on the agenda, there was more important business for the Assembly.

Similarly, Greens MLA Caroline Le Couteur rejected the motion, saying it was a ridiculous piece of theatre and there was really nothing more to say than that the Greens did not support it.

But Opposition Leader Alistair Coe asked the Assembly what in the motion, such as that Ms Fitzharris had overseen a directorate rife with bullying allegations, was not actually true.

The Opposition is expected to again bring forward the motion for debate on Wednesday.