The minister said both sides will be in a "win-win situation" if they cooperate to harness Nepal's hydropower potential.
"Without energy we cannot bring economic prosperity and both India and Nepal can benefit if we work together in developing Nepal's vast hydropower potential, which is God-gifted," he said.
"Nepal can reduce trade deficit with India by selling energy to it. We should work together for mutual benefits," Abdullah said on Friday while inaugurating a three-day trade expo aimed at attracting Indian investments in Nepal's energy and IT sectors.
Nepal is rich in water resources with the potential to generate 83,000 MW of hydropower. It currently generates 674 MW of hydropower from the total installed capacity of 705 MW.
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Nepal and India are already cooperating in the construction of dams on Bagmati, Kamala and Lalbakaiya rivers.
During his stay in Kathmandu, Abdullah also met Nepalese President Ram Baran Yadav and Interim Election Council chairman Khil Raj Regmi. He is the first Indian minister to visit Nepal after the November 19 Constituent Assembly elections.
A flexible and accommodative Constitution will last for a longer period rather than a rigid one, he said.
Speaking at the trade expo, India's former energy secretary Anil Razdan said Nepal should create an investment-friendly environment to attract Indian investors.
"Political consensus and certainty of law and regulation is a must to draw investment from India in the hydropower sector," he said.