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A woman's death while waiting nine hours for a bed at Launceston General Hospital has prompted a concession from Tasmania's premier that the state's health system needs repair.

The woman aged in her 70s was taken to hospital by ambulance on Friday night, but died about 9am on Saturday after being ramped at the emergency department, the union representing Tasmanian paramedics said.

Premier and Health Minister Jeremy Rockliff offered his condolences to the woman's family and confirmed there would be an investigation into her death.

"We can and need to do better when it comes to our health care," he told reporters on Wednesday.

"I know there are challenges. I also know of the wonderful work that happens day in, day out. We need to improve our health system. We're investing in our health system."

The government should be ashamed the woman did not receive appropriate care, Health and Community Services Union industrial manager Robbie Moore said.

He says ambulance ramping is an ongoing issue for the island state, with Tasmanians not receiving appropriate care and paramedics unable to respond to urgent jobs because they're stuck at hospitals.

Mr Moore called on the state government to open more hospital beds immediately.

"In the longer term, they're meant to be negotiating with all their staff when it comes to their wages and conditions," he told AAP.

"We need them to pay competitive wages with the mainland to ensure that we have adequate staff to provide the health services that Tasmanians need."

Meanwhile, the Tasmanian branch of the Australian Nursing and Midwifery Federation has continued strike action on Wednesday over pay and conditions.

Mr Rockliff last week offered a deal to the union in a bid to stop the strike but union members voted to continue the action.

"They continue to be concerned about their workloads and challenges around recruitment and retaining our existing workforce," the federation's Tasmanian secretary Emily Shepherd told AAP.

"We know that many of our members are exhausted. They're burnt out after working in trying circumstances."

The Tasmanian opposition urged the premier to work more closely with health care workers to address the "unprecedented" pressure they're facing.

"Industrial action is a last resort for our exhausted, overworked and underpaid health staff," opposition health spokesperson Anita Dow said in a statement.

"Today's strike... is a direct reflection of the weak leadership of a premier who cannot get the basics right."

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