Anthony Albanese will use a visit to the UN in New York to lobby for Australia to be one of the 10 non-permanent members of the security council.
Australia is seeking a two-year term on the 15-member council for 2029 and 2030.
A vote is not scheduled until mid-2028, but lobbying efforts will ramp up as world leaders gather for the UN General Assembly's high-level week.
Mr Albanese said middle powers such as Australia would play a crucial role on the council as wars in Europe and the Middle East dragged on.
"(The security council) needs reform and it needs to be made more effective; there's no doubt about that," he told ABC's Insiders program from California on Sunday, Australian time.
"Clearly, there's a need for the UN to step up. There's a need for middle powers as well, such as Australia, to exercise the influence that we have."
Two countries are elected to the security council from the Western Europe and Others Group, which includes Australia.
So far, only Australia and Finland have put their hands up for a spot on the council, but other countries from the bloc could still launch bids.
Even if the two countries run unopposed, Australia would still need support from two-thirds of the 193 UN member states to be successful.
Of the 15 members on the security council, China, France, the US, UK and Russia are permanent members, while the remainder serve two-year terms.
Australia would leverage its strong global reputation in its campaign, Mr Albanese said.
"We have, I think, a strong case. We have been prepared to lead the world and to be a part of peacekeeping missions," he said.
"We're the eighth-largest funder of the UN. We think multilateralism is an important part of Australia's foreign policy and the UN needs to be at the centre of that."
Australia was last on the security council in 2013 and 2014, during which time it helped lead the response to the downing of Malaysia Airlines flight MH17.
The prime minister will arrive in New York on Sunday morning, Australian time, ahead of several summits at the UN.
He will make an address to the General Assembly on Friday.
