He calls it "India's gift to the world" and recommends people make yoga as much a part of daily life as their mobile phone. After sweeping to power in 2014, Modi even appointed India's first government minister for yoga.

But yoga is also a key asset in Modi's push to promote and develop India's soft power – described by Harvard academic Joseph Nye as "the ability to get what you want through attraction rather than coercion or payments".

Modi often talks about yoga in speeches and during meetings with world leaders. The day he addressed the Australian Parliament in November 2014 Modi told reporters, "I know yoga is enormously popular here. We need to connect our people more." It was reported Modi discussed the benefits of yoga with US President Barack Obama over dinner at the White House in 2014.

Modi won support from the United Nations for the first international day of yoga on June 21 this year. He marked it with an early morning yoga session with about 30,000 devotees in the north Indian city of Chandigarh. Millions more participated across the world, including thousands in Australia.

"What Mr Modi has been able to do is put an India brand on it through the international day of yoga," said India's High Commissioner to Australia Navdeep​ Suri​. "Hopefully when people think yoga, they will think of India in a positive way."

But there's much more than yoga in India's soft power toolbox. From the glitz and glamour of Bollywood​ to the ancient wisdom of Buddhism, India is flush with cultural attributes that interest and engage people in other parts of the world. It also boasts a 25-million-strong diaspora that is relatively wealthy and increasingly politically engaged. The director of the Australia India Institute, Professor Craig Jeffrey, points out that India has been Australia's largest source of permanent skilled migrants since 2008. "Australia is a lot more Indian than it was 15 or 20 years ago," he said.

For years India's soft power potential remained largely untapped. But Professor Rory Medcalf, a former Australian diplomat to India and head of Australian National University's National Security College, says that is changing.

"It's very clear that the Modi government has been working to harness Indian soft power and Indian cultural appeal more effectively that previous Indian governments have," he says.

Australia will get to sample a little of this cultural charm offensive over the next two months as a program of Indian dance, theatre, music – and of course, yoga – rolls out across seven cities. The Confluence Festival of India in Australia, billed as "the biggest showcase of Indian arts and culture ever to be staged in Australia" is sponsored by the Indian government. Organisers say it will have a "strong and positive impact on the bilateral relationship, fostering mutual cultural connections, promoting tourism and migration and highlighting business opportunities between Australia and India." Modi himself announced the festival during his historic 2014 visit.

Suri, who took up his post as India's High Commissioner in April last year, was previously the head of public diplomacy at the Indian foreign ministry and has been involved with festivals sponsored by the Indian government in South Africa and Egypt.

"I'm a great believer in the power of cultural diplomacy, whether you call it soft power or anything else," he says.

Suri says staging cultural festivals enabled diplomats to "get out of the box" of routine government-to-government interactions.

"What we've found is they have allowed us to very significantly broaden the range of contacts that we have from the narrow bureaucratic circles into the arts, the writers, intellectuals and people who are public figures - culture became a great way to connect with them," he says. "In democracies like India and Australia centres of power are dispersed. It's a 21st century diplomat's task to connect with a much broader range of actors as compared to the traditional diplomacy of engaging on a government to government basis."

Buddhism, Bollywood and India's most potent cultural exports

The rich performance traditions that will feature in the Confluence festival are often overshadowed by Indian cinema. Bollywood has won global recognition and now rates among India's most potent cultural exports. The film industry has a major following in many parts of Asia and the Middle East. India also boasts a cadre of globally renowned writers and public intellectuals including Salman Rushdie, Arundhati Roy and Amartya Sen.

But maybe India's greatest cultural export is Buddhism, which originated in north India and has gradually gained adherents through much of Asia. The region would be very different if not for that ancient manifestation of Indian soft power.

Modi has appealed to the vast Buddhist populations in east and south-east Asia by emphasising India's historic connections to this spiritual tradition. In a speech in September last year he said: "India is taking the lead in boosting the Buddhist heritage across Asia." Indian scholars have dubbed this "Buddhist diplomacy".

"The prime minister is diligently pursuing India's 'Buddhist agenda' and taking it beyond its borders, emphasising the Indian and Hindu links with Buddhism," wrote Indian academic Rishika​ Chauhan​ in a recent paper titled Modi and Buddhism: Between Cultural and Faith-Based Diplomacy.

India's more assertive use of soft power has sparked inevitable comparisons with its giant regional counterpart, China.

Professor Michael Wesley, director of the Coral Bell School of Asia Pacific Studies at ANU, says the key difference is that China starts out with a "significant set" of disadvantages.

"China has an authoritarian regime and people are very aware of that," he says. "India is far from perfect but it doesn't have a Tiananmen Square in its recent past. India is a much more benign presence internationally … it is simply less of a threat."

Wesley says the recent controversies over Chinese influence in Australian politics had underscored a "nasty side" to China's attempts to wield soft power.

"India starts from a much easier position to create positive attitudes," he says.

Medcalf says it would be a mistake for India's "global cultural offensive to look anywhere near as orchestrated" as China's.

"The good news is India is a long, long way from that," he says.

Modi's rhetoric suggests he wants India to exert far more intellectual and cultural influence in future. While addressing a packed audience at Sydney's Allphones Arena in November 2014 Modi said he dreamed of India being a "vishwa​ guru" or guru of the world.

But some are concerned that India's more assertive soft power push is too closely linked to the Hindu nationalism popular with Modi's political power base and a hallmark of his ruling Bharatiya Janata Party. Raja Mohan, one of India's leading strategic analysts, wrote in the Indian Express newspaper that Modi's efforts to project soft power "are likely to come to nought if the government continues to allow a free run to groups that seek to anchor India's rich cultural inheritance on a narrow and religious basis".

Medcalf agrees. Becoming too focused on cultural expressions linked to Hinduism would "dilute" the soft power strengths that set India apart from China.

"There is a risk for India in its global soft power push being too closely associated with Hindu nationalism, or with Hinduism exclusively," he says. "India's great advantage is that it's diverse and democratic."