The two prime ministers are expected to meet on Tuesday evening for the sixth time in 12 months when up to 22,000 supporters gather for a rally centred on Mr Modi at Sydney Olympic Park.
The leaders' regular meetings showed the importance of the relationship between Australia and what will become the world's third-largest economy, Mr Albanese said.
"This is a relationship we need to invest in," he told parliament on Tuesday.
"We have a rich friendship and a very affectionate sporting rivalry.
"We are both part of a growing, dynamic region and Prime Minister Modi is a very welcome visitor to our shores."
He hoped trade discussions concerning the Comprehensive Economic Cooperation Agreement, which began in 2011, would conclude this year and said ties on renewable energy, critical minerals, security and defence were growing.
Mr Albanese also credited the Indian diaspora living in Australia, including about 700,000 people born on the subcontinent, for strengthening the local democracy.
"They have brought the spirit of the world's largest democracy to Australia and helped make our democracy stronger and more inclusive," he said.
As crowds gathered outside Sydney Superdome hours before the evening rally, Mr Modi met business leaders including billionaires Gina Rinehart and Andrew Forrest.
He also discussed infrastructure investment in India and how Australia manages retirement pensions with Paul Schroder, the head of the country's largest superannuation fund, Australian Super,.
But alleged human rights abuses are what some want on the agenda during the whistle-stop tour.
Human Rights Watch's Asia director Elaine Pearson has urged Australia to not to repeat the "same mistakes it made with the Chinese government by pursuing deeper trade engagement while sidelining human rights concerns".
Asked whether human rights should be on the agenda, Deputy Prime Minister Richard Marles said India was a large democracy that shared values with Australia.
"We have never had a greater strategic alignment with India than we do right now. Both countries are deeply invested in the collective security of the Indo-Pacific region," he told reporters in Canberra on Tuesday.
"And all of this is driving a much closer relationship between (the) two countries."
India has snubbed global calls to condemn Russia's invasion of Ukraine, with Moscow remaining a large arms supplier to New Delhi.
Mr Marles used a speech at a defence summit on Monday to say Australia needed to confront "inconvenient truths" with China, as Canberra works to balance competing trade interests with the possibility of military confrontation.
Asked whether the Indian relationship should be approached the same way when it came to calling out human rights abuses and crackdowns on freedom of speech, Mr Marles said the two nations were starkly different.
"We're talking about two very different situations," he said.Â
"We share values with India. India is a democracy.
"I'm not about to go through what will be said or not said in the conversation between our two prime ministers tomorrow, theirs is a very fulsome and open relationship."
The Indian prime minister landed at Sydney Airport on Monday night, greeted by Australia's high commissioner to India, Barry O'Farrell, federal minister Michelle Rowland and NSW Treasurer Daniel Mookhey, who is the son of migrants from the Punjab region.
He's due to meet with Mr Albanese again and Governor-General David Hurley on Wednesday.