During the talks, both Mukherjee and Bhandari hoped that the presidential visit from India, which comes after a gap of 18 years, would help further cement bilateral ties.
While welcoming her Mukherjee at her office, President Bhandari discussed wide range of issues and expressed satisfaction over the present status of Nepal-India ties and underscored regular interactions among the top political leadership, Bharat Raj Poudyal, spokesperson at Nepal's Ministry of Foreign Affairs, told reporters.
Mukherjee told Bhandari that he was eager to host her in New Delhi very soon.
After the meeting, Mukherjee headed to the Indian Embassy to participate in a reception hosted by the Indian Ambassador to Nepal, Ranjit Rae.
Leading a 60-member team including one state minister, some parliamentarians, senior Indian government officials and security personnel, Mukherjee arrived in Kathmandu at 12.30 p.m.
President Bhandari received him at the VVIP lounge at the Tribhuvan International Airport.
Vice President Nanda Bahadur Pun, Prime Minister Pushpa Kamal Dahal, Minister for Foreign Affairs Prakash Sharan Mahat, Minister for Urban Development Arjun Narsingh KC, political leaders and Nepalese Army high-ranking officers were at the airport to welcome Mukherjee.
On the occasion, a contingent of Nepalese Army offered a guard of honour to the Indian President. A 21-gun salute was also offered on the occasion.
After the special welcome ceremony, President Bhandari and her Indian counterpart proceeded in the same limousine to the President's Office, Shital Niwas.
People were lined up at different places on the sides of the road from the airport to Shital Niwas waving the national flags of both the countries.
The Nepalese government has announced a public holiday in honour of the visiting President.
Mukherjee is also scheduled to hold separate meetings with Vice President Nanda Kumar Pun and Prime Minister Pushpa Kamal Dahal 'Prachanda'.
Later in the evening, President Bhandari will host a state banquet.