Prime Minister Tony Abbott says his government has no plans to introduce a GP fee, dismissing the speculation as a Labor scare campaign.

Labor has marked the 30th anniversary of Medicare by ramping up warnings that the Abbott government is planning to introduce a fee to visit GP clinics.

Prime Minister Tony Abbott, launching Bill Glasson’s by-election campaign in Kevin Rudd’s old Brisbane seat of Griffith, has dismissed the claims as nothing more than a scare campaign.

“Nothing is being considered, nothing has been proposed, nothing is planned,” Mr Abbott told reporters in Brisbane on Saturday.

But state and federal Labor MPs insist the prime minister has not categorically ruled out introducing a GP co-payment, which would require patients pay a mandatory $6 fee per consultation.

Shadow health minister Catherine King said the Liberal Party had opposed the introduction of MediCare and were already proving in government they couldn’t be trusted to protect the health system.

“Unfortunately each time the Liberals gets back in government it’s been up to Labor to defend the legacy of Medicare,” she told reporters in Brisbane on Saturday.

Labor’s candidate for Griffith Terri Butler also warned that her Liberal opponent Dr Glasson, a former Australian Medical Association president, had supported introducing a GP co-payment.

But the prime minister said Dr Glasson played a key role helping the former Howard government make reforms to Medicare, and his opponents were trying to smear him.

“Nationally or locally, all they’ve (Labor) got is a scare campaign,” Mr Abbott said.

He said the only person who had cut Medicare in recent years was acting opposition Tanya Plibersek, who as health minister in the former government pulled $1.6 billion in funding for public hospitals.

Australian Greens senator Richard Di Natale said a GP fee would undermine equal and universal access to health care, the very foundation of the Medicare scheme.