Australian Workers' Union (AWU) branch secretary Andy Gillespie yesterday said the "vast majority" of unions supported Mr Jones' stance on same-sex marriage.

He said he believed elements of the Labor Party were using the issue to try to undermine Mr Jones.

"That's not what this debate should be about - it is about fairness and applying the law fairly," Mr Gillespie said.

"Stephen is not isolated in the community and he is not going to be isolated on this issue."

In a veiled swipe at Wollongong MP Noreen Hay, Mr Gillespie said some in the the Labor Party were trying to use the issue to erode Mr Jones' support.

In December, Ms Hay introduced a successful internal party motion attacking Mr Jones' position by highlighting that marriage was between a man and a woman.

"If people want to turn this into a party-room brawl for political ends, it would be a shame to see that happen, that people would try and factionalise the issue for political purposes," Mr Gillespie said.

A 2010 study found support for same-sex marriage was split in Mr Jones' seat of Throsby, with 40 per cent for and against and 20 per cent undecided.

Same-sex marriage advocates are worried about support for Mr Jones' stance in the region.

Peak lobby group Marriage Equality Australia will hold a meeting in Wollongong next month to bolster support for the MP.

Mr Jones is expected to introduce his private member's bill later this year.

Meantime, Attorney-General Nicola Roxon has cleared the path for Australian same-sex couples to wed overseas in countries where it is already legal.

Under the change, same-sex couples will be able to apply for a Certificate of No Impediment, required by overseas governments before they allow a marriage to take place.