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In the 25-minute extempore speech at Parliament punctuated by frequent applause, the Prime Minister said, "There are few countries in the world where we see so much synergy. We celebrate the legend of Bradman and the class of Tendulkar. We are impressed by Australian speed as you are charmed by Indian spin - until of course Shane Warne came along."
Talking about the challenges, he said terrorism has become a major threat for all. "In India, we have seen its face closely for three decades. We can only pursue our dreams if we have confidence that our cities are safe, our nations are secure, our region is stable and our world is peaceful."
The Prime Minister's address came after India and Australia signed five agreements in the areas of social security, transfer of sentenced prisoners, combating narcotics trade, arts and culture, and tourism.
PM Modi has also sought an early closure of India-Australia nuclear deal to facilitate the import of uranium. The two countries had sealed the landmark civil nuclear deal that will facilitate the sale of uranium to India during Mr Abbott's Delhi visit in September.
During the joint statement after the signing of the agreements, PM Modi said, "This is a natural partnership. Huge opportunities of partnership in every area we can think of."
"The economic climate in India has changed and it will be easier to change opportunities into outcomes," the PM said. India, he added, will hold a "Make in India" show in Australia next year. Australia will hold a business week in India in January.
Mr Abbott, who referred to the Indian PM by his first name, said, "Trade means jobs, trade means prosperity, we both need more jobs and prosperity... There are two 'can-do' prime ministers in this chamber today. We can make it happen."
PM Modi had reached Canberra late in the night and in a departure from protocol, was received by Australian foreign minister Julie Bishop. On Tuesday morning, he visited the Australian War Memorial with Mr Abbott.
The visit comes on the heels of his blockbuster reception in Sydney, where he addressed a 20,000-strong crowd at the Allphones Arena of the Olympic Park. Earlier, he had attended the G-20 summit in Brisbane.
The Prime Minister has left Canberra for Melbourne where he will meet top Australian business leaders. After his four-city visit to Australia, he will visit Fiji, before returning to India.
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