Modi, who has been holding diplomatic conversations in Hindi after becoming Prime Minister four months ago, spoke in Hindi during his 35-minute maiden address at the UNGA.
Vajpayee, who was Prime Minister from 1998 to 2004, was the first Indian premier to speak in Hindi at the UNGA's Millennium Summit.
As foreign minister in the Janata party government, Vajpayee had addressed a UNGA session in 1977 in Hindi.
Hindi is not among the official languages of the UN.
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During his address, Modi spoke about Indian culture and ethos.
"It is a truly a great honour to address you for the first time as the Prime Minister of India. I stand here conscious of the hopes and expectations of the people of India," he said.
Talking about India, he said, "India is a country that constitutes one-sixth of humanity; a nation experiencing economic and social transformation on a scale rarely seen in history.