"A royal summer in Delhi! PM @narendramodi receives the Duke and Duchess of Cambridge at Hyderabad House," external affairs ministry spokesman Vikas Swarup tweeted along with pictures of Modi with Prince William and Kate.
During his visit to Britain in November last year, Modi was hosted to a lunch banquet by Queen Elizabeth II.
The royal couple, who arrived in Mumbai on Sunday, attended a reception hosted by the British high commissioner here on Monday to mark Queen Elizabeth II's 90th birthday that falls next week.
The Duke and Duchess of Cambridge are scheduled to leave for Assam later on Tuesday where they will visit the Kaziranga National Park, a Unesco World Heritage Site.