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India's Prime Minister Narendra Modi reacts as he speaks to members of the Australian-Indian community during a reception at the Allphones Arena located at Sydney Olympic Park in western Sydney on Nov. 17, 2014. Reuters/Rick Stevens

(Reuters) - Last week Mick Jagger, this week Indian Prime Minister Narendra Modi.

Thousands of expatriate Indians thronged Sydney's Allphones Arena on Monday, many travelling 1,000 km on a train dubbed the Modi Express, to clap and cheer India's best-known leader since independence figure Mahatma Gandhi.

"I know that behind this affection lie expectations," Modi told the excited crowd. "We want to create the India you are dreaming of."

Modi's appearance at the 21,000-seat arena, which hosted the Rolling Stones last week, underscored the rock star status he enjoys among some Indians at home and abroad.

He promised lifetime visas to people of Indian origin, repeating an offer he made to expatriates in the United States that would seek to strengthen cultural and business ties between overseas Indians and their home country.

"He is very inspiring," said Mustafa Jamnagarwala, one of those listening to Modi's 90-minute address.

"He has a magnetic personality and he makes a lot of sense," said Jamnagarwala, who migrated to Sydney 1-1/2 years ago from Pune. "Now I know if I invest back home my money is safer."

Modi arrived on Friday for the G20 economic summit, where he reportedly pushed the issue of "black money", or funds illegally deposited in overseas banks to avoid tax.

About 300,000 Indians live in Australia, but trade between the two countries stands at around $15 billion a year, or just a tenth of that between Australia and China.

Modi urged overseas Indians to boost investment at home, reprising an appeal made elsewhere, including the United States, where he sold out New York's Madison Square Garden in September.

He took office in May vowing to create jobs and ignite the Indian economy after years of sluggish growth, launching signature initiatives such as 'Make in India' and 'Clean India'.

Modi often reminds voters of his humble roots as the son of a railway-station tea vendor, in contrast to the privileged circumstances of the Nehru-Gandhi dynasty that has dominated Indian politics since independence from Britain in 1947.

Australia is emerging as a key source of thermal coal for India's growing number of electricity users, as they give up older fuels such as wood and kerosene.

Indian trade and infrastructure conglomerate Adani Enterprises has signed a pact for a loan of up to $1 billion from the State Bank of India for a $6 billion Australian coal mine, rail and port project.

Another Indian conglomerate, GVK, and Australian billionaire Gina Rinehart, have won an environmental permit for a second coal mine in Australia, costing $10 billion.

But Modi still has some way to go in winning over potential investors.

"He is expecting people to contribute," said Santosh Kashid, who migrated to Sydney 10 years ago. "However, unless you make India a place to live and work it won't be possible to attract people back home."