Prime Minister Narendra Modi on Wednesday raised with his Australian counterpart Anthony Albanese India's concerns over incidents of attacks on temples and activities of pro-Khalistani elements in Australia, even as the two sides aimed to firm up a comprehensive trade pact by the end of the year.

After wide-ranging talks between Modi and Albanese, India and Australia inked a migration and mobility partnership pact that is aimed at promoting two-way mobility of students, academic researchers and business people and preventing illegal migration.

The discussions that took place on the third and final day of Modi's visit to Australia focused on the entire gamut of bilateral engagement as well as the possibility of cooperation in new areas such as critical minerals and renewable energy.

Modi and Albanese also witnessed the signing of the terms of reference of the Australia-India Green Hydrogen Taskforce which will explore opportunities in the area of renewable hydrogen.

In his media statement in the presence of Albanese, Modi said the bilateral relations are based on "mutual trust and respect" and that the Indian community in Australia is a "living bridge" between the two countries.

"Prime Minister Albanese and I have in the past discussed the issue of attacks on temples in Australia and activities of separatist elements. We discussed it today also," he said.

"We will not accept any elements that harm the friendly and warm ties between India and Australia by their actions or thoughts. I thank the prime minister for the actions that have already been taken. Prime Minister Albanese has once again assured me today that he will take strict actions against such elements in the future also," Modi said.

The prime minister used a cricket analogy to describe the fast-expanding India-Australia ties, saying the relations have entered the "T-20 mode".

"I am visiting Australia within two months of the visit of my friend, Prime Minister Albanese to India. This is our sixth meeting in the past one year. This reflects a depth in our comprehensive relations, convergence in our views, and the maturity of our ties," he said.

"In the language of cricket, our ties have reached the T20 mode," Modi said. "The India-Australia friendship is a special one." He also invited Albanese and Australian cricket fans to India for the Cricket World Cup tournament which is taking place in the country later this year.

Describing his meeting with Albanese as "constructive", Modi said they deliberated on taking the Australia-India comprehensive strategic partnership to "greater heights" in the next decade.

"Last year, the India-Australia economic cooperation and trade agreement came into effect. Today, we have decided to focus on a comprehensive economic cooperation agreement (CECA). This will further strengthen our economic partnership and open up new avenues for cooperation," he said.

In his remarks, Albanese said the aim is to conclude the CECA by the end of the year.

"We reiterated our shared ambition for an early conclusion of the Australia-India comprehensive economic cooperation agreement later this year," he said.

Modi said the India-Australia relationship is not just limited to the two countries as it is also linked to regional stability, peace and global welfare.

"We had constructive discussions on strengthening our strategic cooperation in the sectors of mining and critical minerals. We identified concrete areas for cooperation in the renewable energy sector," he said.

The two prime ministers also reiterated their commitment to an open, prosperous and secure Indo-Pacific.

"India-Australia cooperation can be beneficial for the growth of Global South also. The Indian tradition of Vasudhaiva Kutumbakam that views the entire world as one family is the central theme of India's G20 presidency," Modi said.

In his remarks to the media, Albanese announced the establishment of a new Australian Consulate-General in Bengaluru primarily to connect Australian businesses to India's booming digital economy and innovation ecosystem.

"This is a relationship we need to invest in. Our strong partnership with India will deliver benefits for Australia in trade, investment and business, and in regional security and stability," he said.

Referring to the Quad summit in Hiroshima, Albanese said the leaders of the grouping "stand together for an open, stable, secure and prosperous Indo-Pacific -- a region where sovereignty is respected, and all countries large and small benefit from a regional balance that keeps the peace." The Australian prime minister also spoke about the rapid upswing in the ties between the two countries.

"In my first year as Prime Minister, I have met with Prime Minister Modi six times, which underscores the value we place on deepening ties between our nations," he said.

"Australia is a better place because of the contributions of the Indian-Australian community, and we want to see more connections between our countries," he said.

Albanese and Australian Foreign Minister Penny Wong announced that the new Centre for Australia-India Relations will be headquartered in Parramatta.

The Centre began operations this month and will drive deeper engagement with India through business, policy and cultural activities and work with Indian diaspora communities.

Ahead of the talks, Modi was accorded a ceremonial guard of honour at the Admiralty House in Sydney.

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