The Mersey Community Hospital has a long-term future, new Premier Peter Gutwein says.
The state government took the Mersey back from the federal government in 2017, along with a funding package of $730 million intended to provide for the hospital for 10 years.
Mr Gutwein said he believed the Mersey had a future beyond the federally funded period.
"When that was set up in terms of the way that hospital funding works, with activity based funding at the end of the day, if the state moved to that in 10 years it would be something we could comfortably afford," he said.
"The Mersey's locked down for the period of the arrangement that we have where TASCORP (the Tasmanian Public Finance Corporation) manages that federal payment, but it's the party's position and mine personally that the Mersey will remain open into the future."
The Howard federal government took over the Mersey and its funding in 2007 after a state Labor government started winding down services at the hospital.
Mr Gutwein has said the government needs to do more in areas including health, housing and climate change.
Claims have recently been made that the state's hospital system is stressed partly due to a lack of efficiency and cultural issues, not simply money and rising demand.
Asked about those views, Mr Gutwein said: "I thought the auditor-general made some interesting commentsin the report he brought down last year where he indicated that it wasn't necessarily all about resourcing."
"It can be about culture and management and having an efficient system.
"As a Treasurer, and certainly when Michael Ferguson was the health minister, we have invested significant amounts into health."
Mr Gutwein said health spending had been increasing by about 6 per cent per year.
"We've actually employed nearly 1200 more staff in our hospitals," he said.
"The vast majority of those are doctors, nurses and other allied health professionals, but we've still got pressures and so I think it's important we consider how with that investment we can get better outcomes for Tasmanians and have a conversation about that."