Mr Modi thanked Australia for its support and solidarity during India's fight agains the surge of COVID-19 cases.

"We're supporting them [India] with ventilators and oxygen concentrators. We won't forget India's generosity in exporting vaccines," said Mr Morrison later on Twitter.

The Indian PM also sought Australia's support for the initiative moved by it and South Africa to temporarily relax some Trade-Related Aspects of Intellectual Property Rights (TRIPS) rules for COVID-19 vaccines.

"We agreed on the importance of ensuring affordable and equitable access to vaccines and medicines, and discussed possible initiatives in this regard," said Mr Modi.

The leaders also took note of the progress made in the India-Australia Comprehensive Strategic Partnership since the virtual summit held on June 4 and discussed ways to further strengthen cooperation and foster people-to-people ties.

They discussed regional issues and reiterated the importance of working together for a rules-based international order and a free, open and inclusive Indo-Pacific region.

Australia also announced that it will lift the ban on its citizens who have spent up to 14 days before flying back. The government had threatened to prosecute travellers with a possibility of five years of jail term or a penalty of AUD 66,000 (USD 50,899).

Mr Morrison said they will charter three repatriation flights between May 15-31 for stranded Australians who are the most vulnerable and registered with the high commission and consular offices within India.