The prime minister called for more action on climate change, an end to conflict in Gaza and Ukraine, and alleviating poverty and inequality in a wide-ranging speech to the United Nations on Thursday morning (AEST).
His appeal for greater international co-operation comes at a time when the US under President Donald Trump is increasingly vacating its space as global leader and the rules-based order is threatened by the rise of authoritarianism and regional conflict.
"The creation of the international rules-based order owes much to the post-war leadership of the United States of America," Mr Albanese told the UN General Assembly in New York.
"For the region Australia calls home, that stability has underpinned a generational economic transformation.
"But we cannot ask - and should not expect - any one nation to uphold the rules or guarantee the security on which all of us depend."
His speech came a day after the US president delivered a fiery speech to the UN, lambasting nations like Australia that have recognised Palestinian statehood and telling European leaders: "Your countries are going to hell."
Mr Trump has been leaning on America's allies to pull more of their weight on the world stage amid a perception they are too reliant on US support, but Australia has so far resisted calls to lift defence spending from about two per cent to 3.5 per cent of gross domestic product.
The issue could be discussed when Mr Albanese sits down with US President Donald Trump in Washington on October 20, after months of back-and-forth to secure a face-to-face meeting.
The White House talks were announced after Mr Albanese briefly met the president and posed for a selfie at a reception for world leaders on Wednesday.
The prime minister described their interaction as a "very warm and engaging chat".
Mr Albanese said Australia was investing in defence, development and diplomacy in the Indo-Pacific region, where the US has entrusted it to stave off growing Chinese influence.
He said Papua New Guinea would soon become Australia's newest ally, despite a recent bid to sign a mutual defence treaty unravelling during independence anniversary celebrations.
All nations, including middle and smaller powers like Australia, had to maintain faith in the institution of the UN by ensuring its principles were backed up with deeds, Mr Albanese said.
"If the United Nations steps back, we all lose ground," he said.
"If we give people reason to doubt the value of co-operation, then the risk of conflict becoming the default option grows.
"If we allow any nation to imagine itself outside the rules, or above them, then the sovereignty of every nation is eroded."
Mr Albanese reiterated Australia's efforts to secure a seat on the UN Security Council in 2029/30, as well as its bid to host the COP climate conference in 2026.
In his speech, the prime minister urged the world to embrace clean energy, called for a ceasefire and release of hostages in Gaza, and supported the Coalition of the Willing's efforts to secure peace for Ukraine on their terms.
But no mention was made of the pivotal AUKUS deal with the US and the UK, which would see Australia gain possession of nuclear submarines.
The US is reviewing the three-country agreement to ensure it aligns with Mr Trump's "America First" agenda.
Mr Albanese is due to meet his Sri Lankan counterpart and potentially sit down with Turkey's strongman leader, Recep Tayyip Erdogan, on his last full day in the US, before flying out to London to meet British counterpart Keir Starmer and King Charles III.
