Western Australia's premier has left the door open to compensating the family of Aishwarya Aswath while revealing some financial support has already been provided.
Seven-year-old Aishwarya died of sepsis on Easter Saturday 2021, hours after presenting to the Perth Children's Hospital emergency department with a fever and unusually cold hands.
An inquest was told she had been left in a waiting room for more than 90 minutes, despite her mother Prasitha Sasidharan and father Aswath Chavittupara pleading with clinicians to escalate care.
Deputy State Coroner Sarah Linton found there was a chance Aishwarya's life might have been saved if not for overburdened staff missing repeated opportunities to identify the seriousness of her condition.
Her parents are understood to be seeking a multi-million dollar ex-gratia payment from the state government.
Premier Mark McGowan said the government would consider what it could provide.
"We've already been supporting the family financially. We'll examine what more we can do," he told ABC radio on Tuesday.
"Obviously it's a very sensitive matter and it's a tragic situation and they're a family that's been through a lot of grief and pain."
The premier rejected calls from Aishwarya's parents for a royal commission into the health system, noting there had already been three inquiries into the girl's death.
"I don't think a further inquiry is needed. Royal commissions are very expensive, they cost many millions of dollars," he said.
He also ruled out the removal of long-serving health department director-general David Russell-Weisz, saying it would not be a productive change.
The coroner did not make any individual adverse comment against the staff members involved in Aishwarya's treatment.
But she noted there were multiple opportunities where clinicians could have escalated her care, including when a junior nurse observed Aishwarya to be grunting in pain with an elevated heart rate, respiratory rate and temperature.
The nurse was unable to monitor her because she was repeatedly called away on other duties, including assisting a patient resuscitation.
Among Ms Linton's recommendations was the establishment of a supernumerary resuscitation team in the Perth Children's Hospital emergency department.
Health Minister Amber-Jade Sanderson initially claimed the team had already been implemented but was forced to retreat, admitting rostered ED staff were still being drawn away from their duties to perform resuscitations.
She blamed the mistake on poor advice from the Child and Adolescent Health Service and promised the team would be properly established.
Aishwarya's mother urged the government to act on the coroner's recommendations immediately.
"Every mother should be cherishing their children's achievements and sharing their children's happiness but I am holding my daughter's death certificate and inquest report," Ms Sasidharan told reporters.
"I'm just asking the authorities please implement those recommendations if they think that will help and please make sure another mother (does not) have to go through the same thing."