Welcoming Rajapaksa in India, Modi said, "I congratulate him on his victory in the polls. This is an honour that he chose India for his first trip abroad. This reflects deep friendship between us."
He stated that a stable and prosperous Sri Lanka is not only in the interest of India but also the Indian Ocean region.
"My government's neighbourhood-first policy gives Sri Lanka the top priority. We have decided that multi-faceted cooperation between us will be strengthened," Modi said.
For countering terrorism, Modi said, "India has always opposed terrorism and expects action from international community on cross-border terrorism."
About Tamil people living in Sri Lanka, Modi said, "I am hopeful that the process of integration of the Tamil ethnic community is taken forward."
India had earlier offered Sri Lanka $100 million credit line for solar energy.
Gotabaya Rajapaksa said discussions with Indian counterparts were cordial. "Security was priority. We look forward to enhancing the capabilities of intelligence agencies. We have to rethink our national security strategy. Prime Minister Narendra Modi's assurance is welcoming," the Sri Lanka president said.
"We will continue to work closely with India to ensure Indian Ocean remains safe. We discussed how Sri Lanka could benefit from India in certain areas of economic growth. I thank him for support," he said.
He said he would take steps to facilitate the release of Indian boats in the custody of Sri Lankan authorities. He also thanked India for offering $400 million credit to enhance infrastructure.
"When I was elected, the first official invitation came from India. I am thankful. I would take this opportunity to invite Prime Minister Narendra Modi to Sri Lanka," he said.
Earlier in the day, Rajapaksa said he would make a strong attempt to take Sri Lanka and India relationship to a very high level.
"We are looking forward to working together on issues related to security and welfare of our people," the Sri Lanka President said during interaction with the media after a ceremonial welcome at Rashtrapati Bhavan.
External Affairs Minister S. Jaishankar also met Rajapaksa earlier in the morning.
Rajapaksa arrived in New Delhi on Thursday, in his first overseas tour after taking over as the President of Sri Lanka a few days ago.
He is in India for a three-day official visit to discuss ways to strengthen bilateral ties in key areas. Rajapaksa is accompanied by a delegation, which includes his country's Foreign Secretary Ravinatha Aryasinha and Treasury Secretary S.R. Attygalle.
( With inputs from IANS )