Indian Prime Minister Narendra Modi(R) meets with Apple CEO Tim Cook during a meeting in New Delhi on May 21, 2016

Apple chief executive Tim Cook met with Prime Minister Narendra Modi in New Delhi Saturday, launching a new version of the Indian leader's eponymous app on a visit aimed at pushing the technology giant's expansion plans.

Cook, shown in a video using the premier's gold-coloured iPhone, launched an update to the Narendra Modi Mobile App to include a new volunteering network.

"Thank you @tim_cook! Friends, welcome & happy volunteering. Your views & efforts are always enriching," the prime minister tweeted afterwards.

Apple does not currently have any stores in India, instead selling phones through third-party retailers such as Vodafone and Airtel, but has applied for permission to open shops.

Cook used the meeting to raise the possibilities of manufacturing and retailing in India, as well as tapping its great software expertise for development, the government said.

"Thanks PM @narendramodi for a great meeting. Already looking forward to next visit to India. Best wishes on the app!" Cook tweeted.

The Apple boss has spent several days in the country after jetting in from China, in a visit seen as an extended Asia charm offensive.

He has announced investments including an app design centre in the southern technology hub of Bangalore and a mapping development office in Hyderabad.

India is a compelling market for the technology giant, with nearly a billion Indians—among a population of 1.2 billion—still not online, especially as sales of the iPhone slow in more saturated markets.

Yet Apple products are too expensive for the vast majority of Indians, with taxes taking the cost of a basic iPhone to almost $600.

In April Apple reported its first drop in global iPhone sales since launching the smartphone in 2007.

During his trip to China, Cook announced Apple had invested $1 billion in Chinese ride-hailing app Didi Chuxing, rival of US-based Uber.