Foreign Minister Julie Bishop, in New York for the UN General Assembly, says the seat would promote greater international cooperation to tackle global-security challenges.
And, for the first time, Australia will also bid for a seat on the UN Human Rights Council.
But the announcement has received a mixed reaction.
Foreign Minister Julie Bishop has used her keynote address at the United Nations General Assembly to outline Australia's first-time bid for a seat on the UN Human Rights Council.
The bid would be for the years 2018 to 2020.
Ms Bishop says Australia having a seat on the Human Rights Council would reflect Australia's inclusive, diverse society.
She says it would build on what she calls the Australian government's strong domestic human-rights agenda.
"Our focus would be on empowering women and girls, strengthening governance and democratic institutions, promoting freedom, freedom of expression, and advancing human rights for all. Australia would be at the forefront of efforts to hold to account those responsible for human-rights abuses and to build more effective, preventative and accountability measures. We would be unrelenting in our efforts to secure abolition of the death penalty."
Acting Opposition Leader Tanya Plibersek says serving on councils can enhance Australia's reputation as a good global citizen and let Australia make solid contributions to the world.
However, she says Labor believes the effort to secure a spot on the Human Rights Council will be fraught with difficulties.
"When we are actually going backwards on climate change, we've had the largest aid cuts in the history of Australia, taking us down to the least generous aid budget since we've kept records, and we've also had concerns around our treatment of asylum seekers and refugees."
Kon Karapanagiotidis is chief executive of the Asylum Seeker Resource Centre.
He says Australia should not be rewarded with a place on the Human Rights Council because it is a place for governments that take human rights seriously.
"We're a country that threatens to jail whistleblowers who expose human-rights abuses, locks refugees off on offshore detention centres where women and children are raped, has the world's worst incarceration rates for indigenous people anywhere in the world, (has) Close The Gap that hasn't been dealt with, and continues to fail to tackle in any meaningful way the epidemic of male violence against women."
And the Government has announced its intention to bid for a seat on the UN Security Council.
That council includes 10 non-permanent members, with five elected each year.
The United States, China, France, Russia and Britain make up the five permanent members of the Security Council.
That bid is further away, with the 2029-2030 seat the first one available that is currently uncontested.
Ms Bishop says putting Australia forward this far in advance to serve as a non-permanent member will make it easier to obtain.
"It is appropriate for us to give notice of our intention to campaign for a seat, because these are highly competitive campaigns, and we don't want to spend unecessary time and resources trying to campaign at an earlier slot."
Australia's last two-year term ended in December last year.
Mr Bishop says Australia made a significant contribution through its temporary position on the Security Council.
She says most notable during that time was Australia's advocacy over the downing of Malaysia Airline's flight MH17.
"Had we not been on the Security Council, I doubt very much that we would have been able to achieve that unanimous resolution which led to the presence of Australian authorities and Australian Federal Police in Ukraine to recover the bodies and the remains of the Australians killed on that flight."
Tanya Plibersek says she welcomes the Government's announcement to run for a seat again on the Security Council.
"We think that Australia's reputation is enhanced as an international citizen when we participate in organisations like the UN Security Council. And we believe that the world benefits, too, from our participation. So there's a domestic benefit for Australia, and, also, we are able to make a strong international contribution."
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