Indian Ambassador to Nepal Ranjit Rae called on Prime Minister Oli at his residence here and congratulated him on being elected to the top post.
During the meeting, Prime Minister Oli said Nepal and India are two countries but one society.
He said Nepal-India cooperation is for the mutual benefit of both countries.
Oli also said that he is looking forward to visiting India at an early date.
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Modi was the first foreign leader to congratulate Oli. He also invited Oli to visit India.
The meeting between Rae and Oli comes at a time when there is an unease in the relationship between two countries, since Nepal adopted a new Constitution.
Nepal has alleged that India has imposed an economic blockade on the country following the announcement of its new Constitution, which is being seen as against the interest of Indian-origin Madhesi community living in the Terai region of the Himalayan nation.
At least 40 people have died in over a month of clashes between police and protesters from the Madhesi and Tharu communities and ethnic minorities.
The agitating Madhesi Front claims that the Constitution does not guarantee enough rights and representation to the Madhesi and Tharu communities residing in southern Nepal.
Madhesis are Indian-origin inhabitants of the Terai region bordering India who are also opposed to splitting Nepal into seven provinces.
Oli, a veteran politician and CPN-UML chairman, was yesterday elected as the 38th Prime Minister of Nepal after defeating incumbent Sushil Koirala in a voting in Parliament.