Rajapaksa, who took over as the Sri Lankan President on November 18, has chosen India as the first country of his foreign visit, accepting an invitation extended by Modi soon after his election.
The Indian Prime Minister had sent External Affairs Minister S. Jaishankar to Colombo on November 19 to personally hand over the invitation.
Modi and Gotabaya Rajapaksa held detailed talks here on Friday, covering various aspects of bilateral relations and the reconciliation process underway in Sri Lanka, keeping in mind the interests of ethnic Tamils.
Addressing the media jointly with Gotbaya Rajapaksa after their meeting at Hyderabad House, the Prime Minister underlined India's neighbourhood-first policy and said the Sri Lankan President's visit will boost the age-old ties between the two countries.
He assured Rajapaksa that India is with Sri Lanka in its fight against terrorism and announced a line of credit of $50 million to the island nation for the purpose.
Modi announced another line of credit of $400 million to help strengthen Sri Lanka's economy.
He noted that India is already undertaking a project to build houses for ethnic Tamils in Sri Lanka.
"Under Indian housing project, 46,000 houses have already been built in Sri Lanka and 14,000 more are being constructed for Tamil origin people," Modi said.
"We exchanged our views on reconciliation in Sri Lanka. President Rajapaksa told me about his inclusive political point of view on ethnic harmony... I hope and believe the Sri Lankan government will take forward procedure of reconciliation to fulfil ambitions of equality, justice, peace and respect for Tamil citizens of the country," the Prime Minister said.
The process of reconciliation includes implementation of 13th Amendment, Modi added.
On the occasion, Rajapaksa said the Indian boats seized by Sri Lankan forces will be released.
( With inputs from IANS )