According to the reports, both the leader propelled the peace talks in the Indian Ocean and being mindful of each other's concerns and aspirations for the stability of the region.
The two leaders expressed their unwavering commitment and support for increased cooperation in combating terrorism both within the region and elsewhere.
Prime Minister Narendra Modi with Maldivian president Ibrahim Mohamed Solih. His term is expected to continue until 2023.
The new president of the Maldives took office on Saturday, declaring the state coffers to have been looted and warned that the country was in financial difficulty after racking up debt with Chinese lenders in an infrastructure boom.
Sources said India was the only country mentioned in President Solih's speech and that as a special gesture, the Maldivian President held his meeting with PM Modi immediately after the swearing-in.
Prime minister Modi extended an invitation to President Solih to make a State Visit to India at his earliest convenience.
Solih's Maldivian Democratic Party (MDP) has pledged to end what it called "China's colonialism" and to resist a "land grab" in the country which straddles key East-West shipping routes.
PM Modi has also invited Solih to visit India.
Announcing the visit, Ministry of External Affairs Spokesperson Raveesh Kumar had last week said, "Prime Minister has accepted the invitation with pleasure".
'We were more than soulmates': Diddy's 'nightmare' after ex's death
The former model and occasional actress was pronounced dead at her home on Thursday, 15 November after going into cardiac arrest. I ask you to give the families privacy during this time'.
During the swearing-in, Nasheed sat beside Modi and the two were seen chatting animatedly.
Under Nasheed, relations between India and the atoll nation had improved greatly.
Maldives President-elect Ibrahim Mohamed Solih and his wife Fazna Ahmed arrive at the swearing-in ceremony in Male, Maldives November 17, 2018.
China has said it hoped there would be continuity in policies during Solih's presidency and it would create good conditions for Chinese firms. Modi interacted with leaders from the Maldives and other parts of the world during the oath taking ceremony.
"India and Maldives share a strong partnership rooted in history, strong bonds between our peoples, and their shared aspiration for peace and prosperity". The press statement emphasized that India would assist Maldives in "every possible way.as per requirements of the Maldives". Moreover, Modi welcomed the expanding opportunities for Indian companies to invest in the country in different sectors for the mutual benefit of both countries.
Sri Lanka is also sending Minister of Foreign Affairs Dr Sarath Amunugama and Minister of Provincial Councils, Local Government and Sports Faiszer Mustapha.
Mahinda Rajapakse, Sri Lanka's prime minister when Colombo took out the loans, is looking to return to power in the severe current political crisis gripping the island nation.
Modi was given a red-carpet welcome and greeted at the airport by Maldives Parliament's new Speaker Qasim Ibrahim.