“Cook shared Apple’s future plans for India,” according to a statement from the Indian government.
“He spoke of the possibilities of manufacturing and retailing in India,” the government statement said.
The Apple chief executive on his first trip to India opened a development centre, dined with Indian celebrities and met corporate executives.
Mr Cook’s four-day visit comes as Prime Minister Modi’s administration reviews Apple’s application to open retail stores in the world’s second-largest mobile population.
Mr Modi in a Twitter post on Saturday thanked Cook after the Apple executive launched an updated version of a mobile application named after the premier.
Mr Cook in return thanked Mr Modi for a “great meeting”.
“Already looking forward to next visit to India,” he wrote on his Twitter account.
The men also discussed Mr Modi’s initiatives for renewable energy, according to the statement.
Mr Cook has left India and visited an Apple store in Dubai, according to pictures posted on his Twitter feed.
An Indian telecommunications ministry official had said earlier this month that the country had rejected Apple’s request to import and sell refurbished iPhones to Asia’s third-largest economy.
India is a market where most phones are bought outright and aren’t subsidised by carriers through bill-calling plans.
The challenge for Apple is that its products are beyond the reach of many in India, where most people live on less than $3.10 (€2.76) a day, according to World Bank figures.
As China’s market becomes more saturated and people across the globe upgrade their smartphones less frequently, Apple, Samsung Electronics and other vendors are keen to sell to India’s middle class, which is projected to quadruple to 200m by 2020.
Mr Cook’s every move in India had been covered by paparazzi since he hed begun the visit last Wednesday in the financial capital Mumbai, keeping Mr Cook’s bodyguards busy as the Apple chief executive toured the city’s most famous temple.
He flew to Hyderabad on Thursday, opening a development centre with a prominent politician, before jetting off to another city to watch a cricket match.
Just about every step has has been reported, photographed and tweeted.