India's prime minister has dismissed al-Qaeda's plan to set up a South Asia branch, saying it was "delusional" to think the country's Muslim minority would follow orders to wage a struggle based on religion against their country.

It was Narendra Modi's first reaction to al-Qaeda chief Ayman al-Zawahiri's announcement this month that the group would set up a new operation to take the fight to India, which has a large but traditionally moderate Muslim population, as well as to Myanmar and Bangladesh.

"They are doing injustice towards the Muslims of our country," Modi, 64, who led his Bharatiya Janata Party (BJP) to a landslide victory in India's general elections in May, said in an interview with broadcaster CNN on Friday.

"If anyone thinks Indian Muslims will dance to their tune, they are delusional. Indian Muslims will live for India, they will die for India - they will not want anything bad for India."

There have been relatively few reports of young Indian men leaving to fight causes abroad, which experts say is because local grievances have kept them at home.

Indian Muslims will live for India, they will die for India. Prime Minister Narendra Modi to CNN Modi's BJP was accused by its rivals and some commentators during the election campaign, which it won, of trying to polarise votes along religious lines. He said the threat from armed groups was "a crisis against humanity, not a crisis against one country or one race".

"We have to frame this as a fight between humanity and inhumanity, nothing else," Modi told CNN's Fareed Zakaria.

In the run-up to a visit to the US, Modi also said the world's two largest democracies were natural allies.

He acknowledged there had been "ups and downs in our relationship" but said that both countries shared common values.

"India and the USA are bound together, by history and culture. These ties will deepen further," Modi said.

He said that the US history of immigrant absorption and the vast Indian diaspora showed the people of both countries were inherently tolerant.

"America has absorbed people from around the world, and there is an Indian in every part of the world," Modi said.

"This characterises both the societies. Indians and Americans have co-existence in their natural temperament."