Sharif and Modi shook hands and exchanged pleasantries during their photo opportunity before moving inside for bilateral talks in the presence of officials from both sides.
Both are expected to hold consultations on issues of mutual interest to the two countries.
In the morning, Modi met leaders from Afghanistan, Maldives, Sri Lanka, Bhutan, Mauritus and Nepal.
Modi is due to meet Bangladesh Parliament Speaker Dr. Shirin Sharmin Chaudhury after his meeting with Sharif.
Earlier, Modi started his day by assuming charge at the Prime Minister's Office (PMO).
Narendra Modi was administered oath of office and secrecy by President Pranab Mukherjee as India's 15th Prime Minister along with his 44-member Cabinet on Monday evening.