The protesting fishermen also demanded the arrest of the Lankan navy personnel involved in the shooting.
The fishermen alleged there was no proper coordination between Lankan and Indian officials over the issue of fishermen fishing in the Palk Strait.
They demanded the release of all Indian fishermen arrested by the Sri Lankan Navy as also the boats seized by them.
Policemen have been deployed on the island to monitor the situation.
Bridgo, from Thangachimadam in central Rameswaram, was fishing near the islet when Sri Lankan naval personnel allegedly opened fire.
Fisheries Department Assistant Director Kulanchinathan said Bridgo was shot in the neck and died on the spot.
Another fisherman, Saravanan (22), was injured in the firing. The other fisheremen there escaped unhurt and returned to shore, he had said yesterday.
The Tamil Nadu government had recently protested the rise in the cases of its fishermen being arrested by Sri Lanka, saying the Indian government did "not seem to put adequate pressure" on Colombo in the matter.
Noting that there were currently 85 fishermen and 128 fishing boats in Lankan custody, chief minister Edappadi K Palaniswami had urged the Prime Minister to direct foreign ministry officials to take concrete action through diplomatic channels to secure their release.