"Katchatheevu is part of Sri Lanka according to an agreement and hence it was not possible to give it back to India," Sri Lankan Deputy Minister for Child and Women's Affairs Vijayakala Maheswaran told reporters.
As per the 1974 and 1976 agreements, India had ceded Katchatheevu to Sri Lanka.
On the fishing rights of Indian fishermen in Katchatheevu, she said both the nations must work together to resolve the issue.
"Governments of both the countries must work together to devise a permanent solution to the fishermen problem," Maheswaran said.
Vijayakala was at Katchatheevu to participate in the two-day annual St Antony's festival, which began yesterday. She said about 4,500 persons from Sri Lanka and 3,000 pilgrims from India participated in the event.