Apple chief executive Tim Cook met Indian Prime Minister Narendra Modi on Saturday and shared his company's plans to expand in the country while also discussing issues such as cybersecurity and data encryption.

Cook had Tuesday opened his visit to India, one of the world's fastest growing markets for mobile phones, in search of new growth areas for the US technology giant which saw a slump in sales in 2015.

"Mr Cook shared Apple Inc's future plans for India. He spoke of the possibilities of manufacturing and retailing in India," a statement from the prime minister's office said.

Apple imports the devices it sells in India and does not have its own retail stores in the country.

Modi has been keen for the company to set up production facilities in the country, which would boost his government's Make in India campaign to encourage manufacturing.

Modi also sought Apple's support for his "Digital India" initiative that focuses on e-education, health and increasing farmer's incomes.

"Issues regarding cybersecurity and data encryption also came up for discussion. The prime minister encouraged Mr Cook to help the global community to cope with the challenges of cybercrime," the statement said.

During his meeting, Cook also elaborated on Apple's new office in Hyderabad that would focus on the development of maps for devices. The facility is expected to create up to 4,000 jobs.

The Apple chief spoke about the "immense potential for app development" in India. Cook had announced the setting-up of an app design centre in Bangalore soon after he arrived in India from China.

Cook, who was seen using Modi's gold-coloured iPhone, also launched an updated version of the leader's app, which includes a new volunteering network. The Apple CEO concluded his multi-city India tour with his meeting with Modi.

During his tour, Cook took stock of the company's operations, while getting a feel of the start-up culture in India, meeting app developers and getting a glimpse of India's film industry based in Mumbai.

The Indian government recently rejected Apple's request to sell refurbished phones, but in an interview with broadcaster NDTV, Cook indicated his company had approached the government again.

"I found the government to be really receptive on the issue you raised (refurbished iPhones) ... It's like a new phone, because it has a warranty for a new phone and yes we would like to do it here. We do it in the US, we do it in Japan. We do it in many different parts of the world," he said.

Cook's visit comes at a time when Apple is facing a global slowdown and is looking for new growth markets like India, which is viewed as a big opportunity by the California-based firm.

The market for smartphones grew 28.8 per cent in 2015 with the sale of 103.6 million units, according to the International Data Corporation's Mobile Phone Tracker. Apple's share stands at just 2 per cent.

Although India is a small market for Apple, it is one of its fastest growing, with sales surging 56 per cent January to March 2016 year on year.

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