Mr Albanese is holding a round of key talks at the G7 summit as some of the world's most powerful leaders convene, with a rescheduled Quad meeting also on the agenda.
Mr Albanese met with United Nations Secretary-General Antonio Guterres on Saturday and held a bilateral meeting with Mr Biden on the sidelines of the summit in Hiroshima.
Mr Biden told Mr Albanese he was sorry they were not meeting in Sydney after the US president had to cancel his attendance at a planned Quad meeting next week that included the leaders of Japan and India.
"I deeply appreciate the flexibility of meeting me here at the G7 meeting," Mr Biden told Mr Albanese at a press conference.
The president said the two nations were launching a new joint initiative to accelerate the transition to clean energy, including building more resilient critical mineral supply chains.
"This is a huge step forward in our fight against the climate crisis and I want to thank you for your strong leadership and your partnership in this challenge," he told Mr Albanese.
Mr Biden said he looked forward to hosting Mr Albanese for a state visit in Washington DC later this year.
Mr Albanese told reporters action on climate change was "the entry fee to credibility in the Indo-Pacific".
He said many of Australia's neighbours understood climate change was an existential threat.
"We understand that it's an important component of our national security," he said.
Mr Albanese also thanked Mr Biden for his support in the US Congress for ensuring Australia was a domestic source under the US defence production act, referring to Australia acquiring and helping build nuclear submarines under the AUKUS pact.
Mr Albanese earlier discussed with Mr Guterres the importance of supporting small island nations with finance, climate change resilience and adaptation.
The three-day summit spans global peace, including tackling Russian and Chinese aggression, as well as the transition to clean energy and developments in artificial intelligence.
Australia announced a slate of new sanctions against Russian entities and a ban on machinery being exported to Kremlin-controlled areas in a co-ordinated effort with G7 nations to stop the invasion of Ukraine.
"The G7 is a critical body of seven of the world's largest democracies coming together at a time in which we have global instability," Mr Albanese said on arrival in Japan on Friday.
"We have global instability in our security issues with the ongoing illegal Russian invasion of Ukraine, but we also have tension in our own region."
The White House confirmed the third in-person Quad leaders' meeting would take place in Hiroshima on Saturday.
Mr Albanese said while it would be a shortened meeting, a lot of preparation work had already been done.
"We will have, I think, a successful meeting as well as successful bilaterals," he said.