Moments after claiming a historic win over the Kangaroos, Tonga have set their sights on becoming the best rugby league nation by winning the World Cup.

A Tongan invitational side claimed a slice of history when they stunned world No.1 Australia 16-12 in a pulsating Test at Eden Park on Saturday night.

The victory comes a week after Tonga upset Great Britain, and two years after they also knocked off New Zealand during their fairytale run in the 2017 World Cup.

Tonga fell one game short of the final that year, and are now dreaming of lifting the trophy altogether when the tournament moves to England in two years time.

"There's no doubt we can," coach Kristian Woolf said.

"We've just beaten Great Britain and we've just beaten Australia. And we've got a lot of improvement from (Saturday night), too. That was a tough, gritty effort.

"(But you look at our last 10 minutes, at times there I thought we were trying to lose it. We're kicking out on the full, we're offloading tackle-three.

"But at the end of the day what wins games is how you have to hang in and defend, and how tough you want to do that."

Woolf said solving their dispute with the Tonga National Rugby League board was a priority in their quest for world-best status.

Their end-of-season Tests against the Lions and Australia were almost abandoned after players threatened to boycott due to issues with the TNRL.

It wasn't until the International Rugby League stepped in, suspended the TNRL membership and set up an invitational side that their games went ahead.

TNRL officials claimed they were insulted by the actions of the NRL and IRL and urged Tongan fans to veto the invitational team's matches.

"There's been a lot of blokes who call themselves community leaders calling for boycotts and calling for splits in the community. They're not leaders," Woolf said.

"The blokes who actually are leaders are the blokes like Jason (Taumalolo), (Sio) Siua (Taukeiaho), those kinds of guys who unite the Tongan community.

"And what they did (Saturday) showed they're leaders in their actions.

"When we get the right governance in Tonga, we've shown what we're capable of. I'm hopeful that's what happens going forward after a couple of tough months."

Tonga's next match is likely to be during the NRL's representative round next year as part of the Oceania Cup that won't involve the Kangaroos.

Australian Associated Press