GAY and lesbian Australians who fly to New Zealand to get married could have their unions recognised at home if a bill to be put forward by the Greens is passed in parliament.

Greens Senator Sarah Hanson-Young said this morning she would introduce a bill in the Senate as soon as possible when parliament returned on May 14 that would allow international same-sex marriages to be recognised under Australian law.

"Australian same-sex couples are now lining up to get married in New Zealand and the sad thing is they are not going to be recognised here,” Senator Hanson-Young told ABC News 24.

"They shouldn’t have to leave their marriage at the customs gate.

"Let’s recognise overseas marriage here in Australia.”

Senator Hanson-Young urged Tony Abbott to allow a conscience vote for his MPs to "stop blocking others from showing their love”.

But Mr Abbott says his position remains the same on gay marriage, despite New Zealand's overnight vote.

The Opposition Leader said the issue "had been dealt with” by the current Australian parliament following an unsuccessful vote on gay marriage last year.

But he conceded it was likely to come up again in future parliaments.

"My own position on that particular question is pretty well known,” Mr Abbott said this morning.

"It’s the same position as Julia Gillard’s, John Howard’s and Kevin Rudd’s.”

Asked if he believed the issue of same-sex marriage would be key in the upcoming September election, Mr Abbott said people were "perfectly entitled to discuss whatever issues they want in run up to election”.

Mr Abbott, who has a gay sister, said he didn’t believe there would be mass influx of same-sex couples to New Zealand.

"I would imagine that the ordinary ebb and flow of people across the Tasman will continue,” Mr Abbott said.

New Zealand yesterday passed laws to allow marriage for gay, lesbian, bisexual and transgender people in a convincing 77-44 vote.

It was the 13th country to legalise gay marriage and the first in the Asia-pacific.

The bill passed with the support of several conservative MPs with Prime Minister John Key allowing a conscience vote.

Liberal backbencher Kelly O’Dwyer - who has said she supports gay marriage - this morning said a conscience vote would not be allowed by Tony Abbott in this term of parliament.

"Tony Abbott and the Coalition took a position to the last election and unlike this current government we don’t break the promises we’ve made,” she told Sky News.

"Going forward who knows what the position will be.”

Labor MP Nick Champion said those who voted in support of a gay marriage bill that was put to the parliament last year were on the "right side of history”.

The bill, put forward by Labor MP Stephen Jones, failed in the parliament with Prime Minister Julia Gillard opposed to the move and Mr Abbott refusing his party a conscience vote.

Same sex marriage won’t start occurring in New Zealand for at least another four months, while the New Zealand Department of Internal Affairs gets organised for licence applications.