The country is hosting the Purchas Cup for the first time at Western Springs Stadium, with six gay and inclusive teams taking part.
This country is represented by the New Zealand Falcons, who participate in Auckland club rugby.
Falcons captain Jeremy Brankin said tournaments such as the Purchas Cup could help to combat homophobia within the sport, including at a professional level.
"Hopefully in the future, with the work that we're doing and the work that the New Zealand Rugby Union is doing, someone might feel comfortable coming out, or just being a young gay man coming through the ranks, and they get to that higher level of rugby and they just feel comfortable with their sexuality."
Brankin said the Australian teams would be tough to beat.