"The case will be proceeded under the Indian law. Judiciary in the country is independent," Antony told reporters here.
"The incident of shooting down of two hapless fishermen off the coast of Kollam on February 15 was unfortunate and equally condemnable," he said.
"The investigation in the case was progressing on the right direction and the Kerala government was handling it very strongly and powerfully. The Centre had extended full support to the state's initiative," he said.
The arrested Italian marines -- Latore Massimiliano and Salvatore Girone -- have been charged with murder under Section 302 of IPC.
A Special Investigation Team led by Kochi commissioner, M R Ajith Kumar is probing the case.
The victims -- Valentine Jalastine and Ajeesh Binki - - set out to sea in a boat along with nine fishermen from Neendakara fishing harbour.
The two fishermen were allegedly killed by the marines of Italian ship 'Enrica Lexie' when they fired at their boat on February 15.
The Italian authorities have contended that the fishing boat was fired, mistaking it to be a pirate vessel.