Claims a baby died during understaffing at a major hospital and regular checks on mothers aren't being completed are being investigated by Tasmania's health department.

The Australian Nursing and Midwifery Federation has written to the department seeking urgent action to address "dire" staffing levels at the Royal Hobart Hospital.

Health department deputy secretary of hospitals and primary care, Brendan Docherty, has insisted maternity services at the hospital were safe.

He said claims by the federation a baby had died during low staffing came as a "bit of a surprise".

"We've been talking to staff ... people who are managing our systems and our alerts," he told reporters on Wednesday.

"So far, we've found nothing that corroborates the information the (federation) has provided.

"We have systems in place and escalations in place … we can find no record of any untoward clinical event."

The federation claims midwives have repeatedly raised concerns with hospital management about mothers receiving substandard care.

Women have given birth outside of birth suites, regular checks aren't being completed because of staff shortages and babies are losing weight due to infrequent checks and lack of support with breastfeeding, it says.

Mr Docherty said the department had checked rosters and was unable to verify low staffing claims.

He urged midwives with concerns to report them through normal mechanisms or via their manager.

"We continue to investigate. It's early days," he said.

"If there have been (understaffing) occasions, then we absolutely want to hear about it."

Federation state secretary Emily Shepherd said she was dismayed by the department's comments and said it was proof of a broken system.

"Our midwifery members work on this unit 24/7 and have first-hand experience of staffing issues and the challenges that this presents," she said.

"(They) are unequivocal that there are staffing issues and safety concerns that are putting women and babies at risk."

The federation is demanding immediate solutions including filling of all vacancies with agency staff until the jobs can be filled permanently.

It also wants aides and clerks working 24/7 to allow midwives to focus on care rather than "answering the door bell" and cleaning the birthing baths.

Ms Shepherd said if a commitment is not made within a week, the federation could escalate industrial action or lodge a dispute with the Industrial Commission.

The state Liberal government is undertaking a health worker recruitment "blitz" and has placed advertisements in major mainland Australia newspapers.

It has denied claims frontline services will be cut in the 2024/25 budget, to be delivered September 12, as part of efficiencies curbing spending.