Three-time Indian prime minister Atal Bihari Vajpayee has died, current leader Narendra Modi said Thursday of the ailing 93-year-old who had been hospitalised.

"It was Atal Ji's exemplary leadership that set the foundations for a strong, prosperous and inclusive India in the 21st century," Modi said in a tweet Thursday, using a Hindi-language honorific.

"Atal Ji's passing away is a personal and irreplaceable loss for me."