New Zealand MP Louisa Wall is challenging Australian Prime Minister Tony Abbott to pick up the ball on same-sex marriage.

The gay Labour MP, who is a former national representative netball and rugby union player, has released a video urging Mr Abbott to hold a free vote on reform.

"My message to Tony Abbott is don't be afraid of democracy and don't be afraid of the people."

Marriage equality was a topic of its time, she said.

Ms Wall drafted the Marriage (Definition of Marriage) Amendment Bill which made New Zealand the 13th country to allow same-sex marriage and the first in the Asia-Pacific.

MPs cast conscience votes in April 2013, with no instructions from their parties, and the bill passed 77-44.

"We were able to join what is a global conversation in New Zealand because of the members' bill," Ms Wall said.

"And within the context of that bill, what we were really clear about was that every member of parliament had the right to exercise their conscience."

Australia's Labor Party will introduce a private members' bill aimed at legalising gay marriage, in a move designed to pressure Mr Abbott into deciding on whether government MPs will be allowed a conscience vote, ABC reported last week.

The draft legislation is practically the same as the private members' bill the then government MP, Stephen Jones, proposed to the last parliament, which was defeated in 2012.

When in opposition last year Mr Abbott was blasted for describing the push to legalise same-sex marriage as the "fashion of the moment".

Ms Wall released the video when she was in Sydney ahead of the Mardi Gras parade, GayNZ.com reported.

"Some years after taking on Australia on the netball court and rugby field, she has joined forces with Australian Marriage Equality," GayNZ.com said.