The ship has been berthed at Kochi oil terminal, where security has been tightened.
The preliminary assessment of the marine authorities is that armed guards aboard the ship might have fired at the fishing boat on Wednesday mistaking it for a vessel of pirates.
The coastal police has registered a murder case against the crew of the vessel based on the evidence of bullet injuries found on the bodies of the dead fishermen -- Valentine alias Jelestine, 45, and Ajesh Binki, 25 -- during post-mortem.
Fellow fishermen who were in the same boat as Binki and Jalastine, said the boat had 11 fishermen. They had put out to sea from Neendakara in Kollam district.
Italian Consul General in India, GiamPaolo Cutillo, had reached Kochi on Thursday in the connection with the incident and met City Police Commissioner M R Ajay Kumar.
The burial of Jelestine would be conducted today at Moorthakara Parish Church in Kollam district while Binki's body has been taken to Poothural in Kanyakumary district in Tamil Nadu.
The Kerala government had announced a solatium of Rs 5 lakh each to the families of the deceased fishermen. It was also decided to bear all legal expenses for getting due compensation from the owners of the ship.
The Kollam administration also announced an emergency relief payment of Rs 10,000 each to the kin of those killed.
Meanwhile, fishermen's organisations have threatened to lay siege the ship at Kochi harbour demanding penal action against the ship crew.