The death of a patient who allegedly spent two hours waiting for emergency department admission in Tasmania is under investigation.

The state Greens say the woman, who died at the Royal Hobart Hospital on Tuesday, was "ramped" - the process of keep patients in an ambulance before admission to a hospital's emergency department.

"We understand two paramedics were caring for the patient ... as well as four other patients," Greens MP Dr Rosalie Woodruff said in a statement on Thursday.

"The safe ratio is one paramedic per patient."

Department of Health secretary Kathrine Morgan-Wicks said a "patient had died in the emergency medical unit, which is located inside the Royal Hobart Hospital's emergency department on Tuesday".

"As is the case whenever a patient dies in our care, we take this matter very seriously and we give our sincere condolences to the family and friends of this patient," she said in a statement.

"The Royal Hobart Hospital and Ambulance Tasmania will be undertaking a review to fully understand the circumstances around the patient's death.

"This is now a matter for the coroner and further comment would be inappropriate."

The hospital on Wednesday morning announced it had escalated its COVID-19 management plan to level two, after a spike in cases among patients and staff.

As a result, the health department urged people to reconsider presenting to the hospital's emergency department if their situation isn't an emergency.

According to the most recent data from September, 28 per cent of people who presented to the hospital's emergency department were seen on time.

Premier Jeremy Rockliff told parliament he recognised demand challenges in Tasmania's hospitals and said there had been heavy investment in ambulance services.

"We know there can be periods of significant demand. We also understand people in the community are concerned at that increasing demand," he said.

In August, a woman in her 70s died after waiting nine hours while ramped at the Launceston General Hospital in the state's north.