Prime Minister Narendra Modi and Afghan President Ashraf Ghani met here for delegation level talks.
The talks are being held at Hyderabad House.
President Ghani earlier met External Affairs Minister Sushma Swaraj, who called on him at the Dwarka Suite of Rashtrapati Bhavan.
Earlier, Ghani was accorded a ceremonial welcome at Rashtrapati Bhavan.
Several union ministers, including of Commerce and Industry Minister Nirmala Sitharaman, Defence Minister Manohar Parrikar and Health Minister J.P. Nadda, will later call on him. Vice President Mohammad Hamid Ansari will also call on him.
In the evening, he will deliver the keynote address at the Indian Council of World Affairs. He will also formally call on President Pranab Mukherjee and attend the presidential banquet.
On Wednesday, Ghani will hold a business meeting with the India business organisations CII, FICCI and Assocham. He leaves on Wednesday evening.
Ghani arrived in India on Monday night on a three-day state visit, his first after becoming the president seven months ago.