It could end more than a decade of delays to regular shipments of the fuel despite the two countries signing a historic nuclear co-operation pact.
The Indian prime minister is in the country for three days and will later on Thursday address 30,000 members of the Indian-Australian community in what is expected to be a loud rally at Melbourne's Marvel Stadium.
Speaking at a business event in the city alongside Mr Modi, Mr Albanese said for all the "broad affection between our peoples" the relationship between the countries was "underdone, under-explored and under-examined".
"In the last decade or so, that has certainly changed for the better," the prime minister said.
"Prime Minister Modi, your leadership and your personal engagement with Australia has been absolutely central to this change.
"And so has the drive and determination of the business leaders in this room."
While details of the proposed nuclear pact are thin, Australia and India signed a civil nuclear deal in 2014 but regular shipments of uranium haven't occurred amid concerns the fuel could be used for weapons.
The visit shows that while few national leaders can lay claim to drawing a crowd of tens of thousands during an international diplomatic visit, Mr Modi is an exception.
The Indian diaspora throughout Australia are making their way to Melbourne in large numbers for a glimpse of the leader of the world's most populous nation.
Mr Modi was one of three types of people who were "very popular" in his homeland, Canberra India Council chair Deepak-Raj Gupta said.
"Politicians, Bollywood stars and cricket players,'' he said.
"It doesn't really matter who you are if you fall into one of those."
Mr Gupta has travelled to Melbourne with his wife and a contingent of friends to attend as many Modi-related events as possible.
But Mr Modi is also one of the world's most polarising political leaders.
Human rights groups such as Amnesty International have condemned him for declines in India's living standards, including targeting of journalists and academics through anti-terror legislation.
Marginal religious groups including Muslims and Christians have also been targeted.
Nevertheless, Mr Modi was able to unite the Indian diaspora in a way no one else could, Australian Multicultural Action Network president Ravi Krishnamurthy said.
"We look for connection (between Australia and India). There is pride in adding to Australia's multicultural community," he said.
Mr Krishnamurthy said he hoped there would be more conversations about two-way trade and tertiary education deals.
"Businesses here are starting to invest in India," he said.
The Australian Federal Police formally warned a young person who had made a death threat towards Mr Modi ahead of his arrival in Australia.
A far-right influencer also gatecrashed the Melbourne hotel where the Indian prime minister is staying, before being thrown out by police.
He posted a video of his late-night tirade where he yelled "f*** Modi" in the hotel's lobby.
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