Opposition Leader Peter Dutton has declared he supports women accessing abortion, as he attempts to prevent the debate from becoming a key federal election issue.

The Greens announced their own election pledge on Wednesday, promising an extra $100 million a year in funding for public hospitals to provide termination services.

Mr Dutton issued a warning to his partyroom that a fight on abortion would result in the coalition losing votes in 2025.

The debate over access to terminations in Queensland’s election is credited with narrowing the lead the Liberal National Party held over Queensland Labor.

Mr Dutton said despite supporting the right of women to access abortion, he would not require Queensland Nationals senator Matt Canavan and South Australian Liberal senator Alex Antic to withdraw a bill attempting to change the law.

“I’m not advocating that they withdraw their bill or put it forward,” he told ABC radio on Wednesday.

“In most cases, 99 per cent of the cases, the bill won’t get forward unless it’s got the support of the government.

“So if the government’s playing games, then that’s an issue for them. But for us, our senators have a right to put their own bills forward and it can be voted on on that basis.”

Mr Dutton said he had been in “very difficult circumstances” working as a detective in the sex offender squad, and had dealt with women who had been raped.

“Ultimately, that’s a choice and a decision for that individual to make, and that’s the position I support,” he said.

Mr Dutton said abortion laws were handled by the states.

Pointing to “politicised debates” about pregnancy terminations in the Queensland state election and the United States presidential race, the Greens are urging Labor to provide free services across the country.

The party is seeking to ensure abortion remains accessible for all women, and particularly those in regional and rural areas are not denied care.

Many public hospitals do not provide abortions, meaning women are forced to travel or pay for private services, which can cost thousands of dollars.

Greens spokesperson for women Larissa Waters said reproductive healthcare must not be a culture war or a postcode lottery.

“We’ve seen conservatives in Queensland, South Australia and the USA open the culture war again and it’s critical Labor take this opportunity to make sure every person in the country can access the reproductive healthcare they need,” she said.

“The Greens will fund the provision of abortion services and care at no cost through the public health system, and receipt of this new funding will require public hospitals to provide a full suite of reproductive health services, including surgical abortions.”

Senator Waters said the federal government was more than a year late in responding to a parliamentary inquiry’s report into abortion services, which handed down 36 recommendations.

Family Planning Alliance Australia Chair Caroline Mulcahy said abortion was healthcare and should be available in every public hospital.

“Money should not be a factor in the decision to have an abortion or choose to parent, everyone should have universal access to their healthcare choices,” she said.

“Decriminalising abortion was the responsibility of states and territories, now it’s time for all governments to work together to make abortion accessible.”

The ABC revealed earlier in November the public hospital in Orange, NSW had directed staff to no longer provide abortions to patients without “early pregnancy complications”.