Calling Prachanda a "capable" leader, Kumar hoped that he will be able to ensure that there are no fresh flare ups or Madhesi agitations in areas of Nepal bordering Bihar.
He called on Prachanda, who took over as Nepal's Prime Minister for the second time recently, at the Nepalese embassy here.
"There are many issues. Indo-Nepal ties are unique and special. We have discussed the issues related to the rivers in Bihar that emerge from Nepal. The rivers in north Bihar mainly emerge from Nepal.
Kumar said he has also requested the Centre to resume the Patna-Kathmandu flights.
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Besides Kumar, CPI(M) General Secretary Sitaram Yechury and NCP leader D P Tripathi also called on Prachanda.
"I have conveyed to him that as far as CPM is concerned, it will play its due role in order to ensure that the entire constitutional process in Nepal is completed with the maximum satisfaction to all the sections in Nepal.
"The process of the constitutional amendments should be completed so that there is a political stability in terms of the direction Nepal will be taking," he said.