Speaking before pen was put to paper on the statement of intent to advance the two nations' climate cooperation, Biden said the agreement signified an expansion of the alliance between Australia and the United States.
"This statement of intent is a testament to our close, bilateral cooperation. I mean that - close," Biden said.
"We're going to establish climate and clean energy as the third pillar of the Australia-US Alliance.
"This contract can enable the expansion and diversification of clean energy supply chains, especially as it relates to critical materials."
Albanese said climate was a crucial aspect of defence cooperation in the Pacific.
"Many of our neighbours understand that climate change is an existential threat," he said.
"And what we understand is that it's an important component of our national security, and that's why it is an important component, an essential part of our alliance."
A joint statement from the two leaders said the accord signed the day strengthened Australia and the USA's alliance in response to "evolving challenges".
"We are taking urgent action to elevate global climate ambition, accelerate the global clean energy transition, and support mitigation, adaptation and resilience efforts in the Indo-Pacific and beyond," the statement said.
"The compact affirms the position of climate and clean energy as the third pillar of the alliance, alongside our defence and economic cooperation."
During their meeting, the US President also apologised to Albanese for having to cancel his recent trip down under.
"I truly apologise to you, for having you to come here rather than me being in Australia right now," he said.
Albanese said he understood the circumstances.
"I would have done exactly the same thing," he told Biden, adding, "I'm very much looking forward to the state visit."
The bilateral meeting in Hiroshima came ahead of Biden and Albanese's participation in a makeshift Quad leaders summit in Japan, following the US president's withdrawal from next week's now-cancelled conference in Sydney.
Quad leaders unite
When the four leaders of Australia, the US, Japan and India met in Hiroshima, Biden again thanked them for "accommodating the change in location".
Albanese in kicking off the meeting similarly praised the group's flexibility, giving thanks to Indian Prime Minister Narendra Modi and Japan's PM Kishida Fumio for the last minute move of the summit.
"The Quad Leaders coming together in-person sends a strong message about Quad unity and what the group is able to achieve together," Albanese said.
"Australia is always better off when we work together with our close friends and partners, and engage openly and constructively."
During the meeting, Modi called the Quad important for peace and security in the region, while Kishida noted the security environment has become even more severe recently.
The diplomatic partnership of the four countries - committed to promoting stability, resilience and prosperity in the Indo-Pacific - also announced a number of key outcomes following the meeting, which they say demonstrates the "positive, practical agenda".
Along with the clean energy agreement, the Quad also hashed out a health partnership enabling a co-ordinated response to disease outbreaks and other health emergencies in the future.
There will also be the first of its kind advanced telecommunications system deployed in the Pacific to improve digital connectivity they announced.
The announcements "take forward the Quad's work on climate change and clean energy, infrastructure and connectivity, health security, and critical and emerging technology" Albanese said.
The Prime Minister also noted that he looks forward to welcoming his Indian counterpart to Sydney next week.
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