President Pranab Mukherjee and Prime Minister Narendra Modi received Ms Bhandari. She was then given a ceremonial guard of honour at forecourt of Rashtrapati Bhavan.
External Affairs Minister Sushma Swaraj also called on Nepal President Bidhya Devi Bhandari.
"Special honours for a close neighbour," External Affairs Ministry spokesperson Gopal Baglay tweeted while announcing her ceremonial welcome.
Later in the morning, she paid her tributes to Mahatma Gandhi at Rajghat.
PM Modi, External Affairs Minister Sushma Swaraj, Home Minister Rajnath Singh and Finance Minister Arun Jaitley will call on the visiting dignitary on Tuesday.
The Nepal President arrived here on Monday on a five-day visit to India at the invitation of her Indian counterpart Pranab Mukherjee.
This is Ms Bhandari's first foreign tour after assuming office in October 2015.
She is accompanied by a 33-member delegation that includes Foreign Minister Prakash Sharan Mahat and Peace and Reconstruction Minister Sita Devi Yadav, five women lawmakers and senior officials.