"India mourns the unfortunate demise of Marshal of the Indian Air Force Arjan Singh. We remember his outstanding service to the nation," he tweeted.
Modi said the determined focus of Singh, who was promoted to the five-star rank of Marshal of the Air Force in 2002, on capacity building in the IAF added great strength to India's defence capabilities.
"India will never forget the excellent leadership of Arjan Singh in 1965, when the IAF saw substantial action," the prime minister said in a series of tweets.
"Sometime back I met him, who despite his ill health tried to get up to salute even though I said no. Such was his soldier discipline," he said.
He said his thoughts were with Singh's family and those mourning the demise of the distinguished air warrior and a fine human being," the prime minister added.