Mukherjee, who arrived at the Tribhuvan International Airport here, was received by President Bhandari and later they had a meeting at the Sheetal Niwas or Rashtrapati Bhawan.
"The bilateral meeting was warm and cordial," Foreign Ministry officials here said.
"The Indian President also congratulated President Bhandari and the people of Nepal for the promulgation of the Constitution through the Constituent Assembly last year," Nepal's Foreign Ministry spokesperson Bharat Raj Paudyal said.
Their blockade had caused strain in bilateral ties, with Kathmandu accusing New Delhi of imposing an "unofficial blockade" which India had categorically denied.
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The two leaders, during the meeting, focused on matters relating to bilateral relations and they stressed on the need to strengthen friendly ties between the two countries, according to Paudyal.
Mukherjee invited Bhandari to visit New Delhi at the time of her convenience which she accepted, Foreign Secretary S Jaishankar told reporters.
Nepal's Minister for Foreign Affairs Prakash Sharan Mahat, Minister for Tourism and Culture Jeeban Bahadur Shahi and Foreign Secretary Shanker Das Bairagi were also present during talks.
Nepalese Vice President Nanda Bahadur Pun also called on President Pranab Mukherjee, who is here on a three-day visit -- the first by an Indian President in 18 years.
"All aspects of connectivity were discussed but one interesting thing that came up during this time and this was raised by the Vice President and that was connectivity by water. He was talking about connectivity from Kolkata through Hubli, the Ganga and the Kosi and this can come about if Kosi project develops," Indian Ambassador to Nepal Ranjit Rae said.