The prime minister is visiting the United States, the United Kingdom and the oil-rich United Arab Emirates, where a lucrative free trade agreement comes into force.
He will address the United Nations General Assembly in New York for the first time as prime minister.
Mr Albanese is expected to follow the UK and countries such as France by outlining Australia's support for Palestinian statehood.
"Australia played a pivotal role in the founding of the United Nations - because we have always understood how important it is for middle powers as well as smaller nations to have their voices heard in the big challenges facing our world," he said on Saturday."Our sovereignty and prosperity are strengthened through global institutions and rules."
Mr Albanese would also hold "bilateral meetings" with major international partners, his office said in a statement on Saturday, raising the prospect of a highly anticipated tete-a-tete with the US president.
It comes after Mr Trump lashed out at veteran ABC journalist John Lyons and accused him of "hurting Australia very much" for asking critical questions about the president's business dealings.
"Your leader is coming over to see me very soon," Mr Trump shouted at Mr Lyons in a fiery exchange on Wednesday.
"I'm going to tell him about you. You set a very bad tone."
Mr Albanese is hoping to position Australia as a minerals hub to break China's supply chain dominance.
An Australian delegation made up of more than 20 critical minerals companies recently met with Trump administration officials ahead of Mr Albanese's visit.
The prime minister will travel to London for his second stop, where he will meet with British counterpart Keir Starmer, who hosted Mr Trump as part of a lavish state visit.
The UK is Australia's second-largest source of foreign investment and second-largest destination for outgoing investment, Mr Albanese's office noted, and a crucial defence partner along with the US.
King Charles praised the AUKUS pact as "vital" during Mr Trump's visit.
The nuclear submarine partnership would deliver Australia at least eight submarines in the next three decades at an eye-watering cost of $380 billion.
Mr Albanese's final destination will be the UAE, which has emerged as a powerful military and economic force in the Middle East.
He is due to meet with President Sheikh Mohammed bin Zayed Al Nahyan as a crucial free trade agreement inked in 2023 comes into effect.
Emirati tariffs will be cut on 99 per cent of Australian products entering the country - an estimated saving of $135 million in the first year and $160 million annually once the pact is fully phased in.
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