As a close neighbour, India is interested in peace, stability and progress of Nepal, said Mukherjee, who is the first Indian President to visit Nepal in 18 years.
"We have learnt from our own experience that sustainable socio-economic development can only be achieved in an environment of peace, stability and a participatory democracy, and where every section of the society is an equal stakeholder in political processes and the outcomes.
Like any relationship of "this depth and intensity, there are times when we may have differing perceptions on certain aspects," he said on questions about India's position on the Madhesi protests that led to a blockade of border checkpoints and caused shortage of essential commodities in the landlocked country, effectively nosediving the bilateral ties briefly.
Madhesis, the inhabitants of southern plains who share close ties with Indians, had launched months-long agitation demanding more political representation and had alleged the Constitution Nepal adopted in September last year was discriminatory to their interest.
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"But we do manage any such differences with sensitivity, goodwill and utmost understanding of each other's vital interests. This has been the case throughout the history of India-Nepalrelations," he said.
"(And) let us not forget that ours is a unique partnership, which is driven by extensive contacts between our two peoples... As close friends, we, therefore, welcome all efforts that lead to enduring peace and stability in Nepal," he said.
Mukherjee said India's engagement with Nepal will always be guided by the long-term interests of both the countries.
relations between India, Nepal and China, Mukherjee saidIndia has an age-old, multi-faceted and time-tested ties with Nepal.
"Our ties with Nepal have their own natural logic. The open border is its most unique characteristic. We remain open to any ideas, which will be mutually advantageous and enable economic development and well-being of the people of Nepal," he said without commenting of the possibility of a trilateral engagement.
Mukherjee said both the countries have tremendous untapped potential to boost cooperation in hydropower and connectivity.
"An essential dimension of'neighbourhood-first'policy is enhancing connectivity in the region - physical connectivity, digital connectivity, trade and transit facilitation, and exchange of ideas," he said.
Talking about regional groupings like SAARC and BIMSTEC, he made it clear that there is no possibility of cooperation among SAARC member-states under the shadow of terrorrism.
"India continues to attach importance to cooperation within the framework of SAARC. However, no cooperation can take place in an environment of terror," Mukherjee said.
Asked why India seems to be giving greater priority to alternative regional forums like the Bay of Bengal Initiative for Multi-Sectoral Technical and Economic Cooperation (BIMSTEC) over SAARC, he said "our interests lie in fast growth and development. We do not want to get bogged down by the processes or formats."
BIMSTEC comprises Bangladesh, India, Myanmar, Sri Lanka, Thailand, Bhutan and Nepal; Pakistan, a member of SAARC, is not included.
The 19th SAARC Summit scheduled in Islamabad this month had to be cancelled after India opted out following an attack on an army base in Uri in September by terrorists backed by Pakistan. 19 Indian soldiers were killed in the attack.
On Nepal's request to India to allow the Visakhapatnam Port for transport of its goods, Mukherjee said the facility has already been made available to Nepal.