Mr Biden described the two countries as working in lockstep to address challenges including climate change.
Earlier, Mr Biden told the United Nations General Assembly the world was fast approaching the point of no return on climate and pledged to increase US aid.
"I meant what I said. We are at an inflection point, things are changing. We either grasp the change and deal with it, or we're going to be left behind - all of us," he said as he sat alongside Mr Morrison after the address.
UK Prime Minister Boris Johnson is calling for stricter targets to cut emissions, urging humanity to "grow up" and stop "trashing the planet".
Chinese President Xi Jinping told the UN General Assembly his country would not build new coal-fired power plants overseas. Mr Kerry said he was absolutely delighted with the announcement.
Mr Morrison indicated Australia would update its climate commitments ahead of UN talks in Glasgow in November.
"Our achievements in reducing emissions is an important story for Australia to continue to tell," he told reporters.
"We will continue to work on our plan as to how we can continue to reduce emissions to zero well in the future.
"Because in Australia it's not enough to have a commitment to something. You've got to have a plan to achieve it."
A deep schism over climate action has hobbled progress within the Coalition government, amid rising concerns insufficient action poses a risk to Australia's foreign trade.