Kumar, who is here to attend the opening ceremony of the Nepali Congress' 13th national convention to be held tomorrow, called on President Bidya Devi Bhandari, Prime Minister K P Sharma Oli and held talks with UCPN-Maoist Chairman Prachanda.
During the meeting with President, the two leaders discussed various dimensions of bilateral relations, a statement issued by the President's Office said.
During his meeting with Oli, they discussed bilateral ties and mutual cooperation.
Oli expressed happiness about the progress made by Bihar under Kumar's leadership.
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Both the leaders agreed that Bihar is the immediate neighbour of Nepal and they have very close relationship.
Bihar and Nepal share common rivers, natural resources and wildlife.
Oli briefed Kumar about the sequence of political developments in Nepal after the Madhesi-led agitation against the new Constitution.
They also discussed Oli's recent visit to India which Kumar termed as "successful".
Oli said that most of the political problems that arose after the promulgation of the new Constitution have been resolved, according to Prime Minister press advisor Promod Dahal.
According to Prachanda's secretariat, the Indian leader expressed concerns over political developments in Nepal after promulgation of the Constitution including the Madhes agitation in talks with Dahal.
The two leaders agreed that open border-related problems between Nepal and India should be resolved together, the Secretariat said after the meeting that lasted about 45 minutes.
JDU leader K C Tyagi, Indian Ambassador to Nepal Ranjit Rae and senior officials of the Kathmandu-based Indian Embassy were present during the meetings.
A delegation of Madheshi Leaders is expected to meet the chief minister.