Modi also made a fervent plea for peaceful resolution of maritime issues and respect for international maritime rules in comments that came against the backdrop of China seeking to exert influence in the disputed waters of the South China Sea.
The prime minister was speaking at a function after commissioning of the India-built coastal patrol vessel for Mauritius in the presence of his host Prime Minister Anerood Jugnauth.
Touching upon the need for cooperation among Indian Ocean countries, Modi said those who live in the region have the primary responsibility for peace, stability and prosperity in the Indian Ocean.
"But, we recognise that there are other nations around the world, with strong interests and stakes in the region. We seek a future for Indian Ocean that lives up to the name of 'SAGAR -- Security and Growth for All in the Region'," he said.
Stating that the world often defines regional groupings around landmass, Modi said the time has come for a strong grouping around the Indian Ocean.
"We will pursue this with new vigour in the years ahead," he said.
Modi also said there can be no better place to host the Indian Ocean Regional Association (IORA) than Mauritius.
He added he was pleased that the Secretary General of IORA is from India. Currently Ambassador K V Bhagirath is the Secretary General.
The Prime Minister noted that India is deeply engaged with Indian Ocean countries through dialogue, visits, exercises, capacity building and economic partnership.
"Indian Ocean Region is at the top of our policy priorities," he said.
The prime minister said India's goal is to seek a climate of trust and transparency, and respect for international maritime rules.
"Our goal is to seek a climate of trust and transparency, respect for international maritime rules and norms by all countries, sensitivity to each other's interests, peaceful resolution of maritime issues and increase in maritime cooperation," he said.
India has always maintained that there should be a freedom of navigation in the high seas and the territorial dispute in the South China Sea should be resolved through dialogue.
The territorial disputes in the South China Sea involve both island and maritime claims among several countries in the region, including China, Vietnam and the Philippines.