The two sides inked nine MoUs to expand cooperation in a range of areas, including in transport and power sectors.
Read more from our special coverage on "NEPAL INDIA RELATION"
The relationship between the two countries had soured in the wake of the agitation by the India-origin Madhesi community, which shares close family and cultural ties with Indians, opposing Nepal's Constitution.
"The announcement of the new Constitution in Nepal came after decades of struggle in Nepal. It is a major achievement. I appreciate the contribution of the political leadership and people of Nepal for it.
"But its success depends on consensus and dialogue. I am confident on the basis of these principles and through political dialogue and by taking all sections together, you (Oli) will be able to resolve all issues relating to the Constitution satisfactorily and take Nepal forward towards the path of development and stability," Modi said in his media statement, in presence of Oli.
The prime minister said India always wanted peace, stability and prosperity in Nepal and that it would extend all possible help to ensure its all-round development.
On combating terrorism, the prime minister said, "We will not allow terrorists and criminals to use our open border. In this regard the security agencies of the two countries will intensify cooperation."
Oli on his part said India will remain a close friend of Nepal and that the "misunderstandings that persisted between the two countries in the last few months no longer exist".
Modi said it was clear that "Nepal's stability is linked to India's security" and that the two sides agreed to fight growing extremism and terrorism.
The two prime ministers also dedicated 400 Kv Dhalkebar-Muzaffarpur transmission line via "tele-inauguration" from Hyderabad House. India will supply 80 Mw of power through the line to Nepal now and it will be enhanced to 600 Mw in the next two years.
"India's assistance has always been constructive. Our actions have been in line with the priorities of people of Nepal," Modi said.
The prime minister said both sides are working on a number of hydro-power projects in Nepal.
He said trade and investment are strong pillars of relations between the two countries and mentioned about the joint initiatives to construct roads in Terai region which he said will boost trade and infrastructure.
"The earthquake hit Nepal, but its pain was felt by every Indian. Our $1 billion assistance package will take forward our cooperation in this area," he said.
The Nepalese prime minister thanked Modi and people of India for "spontaneous support" in aftermath of earthquake in Nepal last year.
Earlier, Oli was accorded a ceremonial welcome at Rashtrapati Bhavan where Modi was also present.
Before the talks between the prime ministers, External Affairs Minister Sushma Swaraj called on Oli. During the meeting, he conveyed to her that Nepal is and will remain a "reliable" friend of India.
Official sources said Oli told Swaraj that he wants to "move forward in the relationship which is not man-made but entirely natural and civilizational".
Swaraj said the visit will deepen the trust between the two countries.
Swaraj and Oli also discussed reconstruction efforts in Nepal, which was hit by a devastating earthquake in April last year, sources said.
"They discussed political issues, reconstruction assistance, SAARC satellite and bilateral cooperation," the sources said.
Oli is accompanied by wife Radhika Shakya, Deputy Prime Minister and Foreign Minister Kamal Thapa, Finance Minister Bishnu Poudyal, Energy Minister Top Bahadur Rayamaji and Home Minister Shakti Basnet among others.
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