State and territory leaders will push the commonwealth to restore 50-50 hospital funding and increase the Medicare rebate while New South Wales will champion changes to expose doctors to greater competition.

The premiers’ wishlists come before a national cabinet meeting on Friday to consider the Strengthening Medicare taskforce report, which aims to improve the commonwealth-funded primary care system to take stress off state-funded hospitals.

But the federal health minister, Mark Butler, has all but ruled out changes to the Medicare rebate. He has foreshadowed major changes to primary care, which will include funding to encourage “blended” services, such as medical centres offering access to nurses, physiotherapists and other allied health professionals instead of just general practitioners.

The New South Wales premier, Dominic Perrottet, wants a NSW trial for pharmacists to prescribe antibiotics for urinary tract infections, treatments for skin conditions and infections and birth control to be extended nationwide, ending doctors’ effective monopoly on prescriptions.

Perrottet has brushed aside doctors’ resistance to the plan, telling the Sydney Morning Herald he believes they are wrong to oppose it.

“Change is always difficult, and there will always be different opinions and I completely respect that,” he reportedly said.

The South Australian premier, Peter Malinauskas, praised the Albanese government for acknowledging the primary care problem and welcomed the direction of the Strengthening Medicare report, which will be released on Friday.

Malinauskas told Guardian Australia: “The status quo is not satisfactory when it comes to the performance of the health system – particularly the primary health system and the effect it’s having on the hospital system.”

He said states were contributing funding to the healthcare system at an unsustainable pace and the primary care changes needed to translate into substantial action.

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“At some point we have to accept the fact that so many of the levers that inform the number of people that present at emergency departments is directly informed by the performance of the primary healthcare system for which the commonwealth is responsible.”

The Tasmanian premier, Jeremy Rockliff, said he hoped the Strengthening Medicare taskforce would address “the viability issue so many practices are facing due to the low value of Medicare rebates”.

“We know that access to timely, affordable primary health care is critical, and despite the best efforts of hard-working GPs – we are seeing falling bulk billing rates and Tasmanians are having more difficulty accessing GP appointments.

“Although primary healthcare is the responsibility of the federal government, the Tasmanian government is increasingly stepping in, and investing in primary care to enhance access across the state.”

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The Victorian premier, Daniel Andrews, was re-elected in November on a pledge of a 12-month pilot project from the middle of 2023 to expand the role of community pharmacists to treat minor health conditions.

Andrews said Medicare “should be fast, free and local and we’re looking forward to discussing this issue” at national cabinet.

“Despite primary care being a Commonwealth responsibility, the Victorian government has been stepping in with our priority primary care centres, which are free clinics hosting salaried GPs that see hundreds of patients each week, reducing pressure on busy emergency departments and giving patients access to the care they need before they become acute,” he said.

“We know what the solutions to Australia’s broken primary care system are – we urgently need to pay GPs more, increase university places to get a pipeline of new doctors across the nation, attract GPs from overseas to Australia faster – and break down the barriers between primary care and our hospital system.”

Since ending the temporary 50-50 hospital funding split agreed during the first two years of the Covid pandemic, the federal government has not been keen to revisit the national health reform agreement, which runs until 2025.

On Tuesday Butler continued to play down the possibility that primary care could be funded beyond Labor’s $750m Strengthening Medicare fund, saying: “Simply putting more money into the existing structures is not going to deliver the type of care modern Australia needs.”

Butler said the government would establish 50 urgent care clinics and the taskforce would identify “the best ways to boost affordability, improve access, and deliver better support for patients with ongoing and chronic illness”.