But Australia's Foreign Affairs Minister Julie Bishop has been reported as saying that approach was counterproductive.
"The reality is that disarmament cannot be imposed this way", the Sydney Morning Herald reports her saying.
"Just pushing for as ban would divert attention from the sustained, practical steps needed for effective disarmament."
But the recently declassified documents reveal the Australian Government's main concern was that a nuclear weapons ban would "cut across" Australia's dependence on the US nuclear arsenal as a key part of its defence position.
An Australian Foreign Affairs and Trade department document endorsed by Ms Bishop last year says a nuclear weapons ban "conflicts with Australia's long standing position that, as long as a nuclear weapons threat exists, we rely on US nuclear forces to deter attack on Australia".
The documents cited by the Sydney Morning Herald show the Australian Government was frustrated when Japan decided to back the New Zealand led statement at the UN and indicate Washington reprimanded Tokyo over that decision.