She spoke after talks with her Italian counterpart Steffan de Mistura.
Italy says as the incident took place in international waters the men should be tried in Italy. Officials say the fishing boat was behaving aggressively and was mistaken for a pirate vessel.
Italian officials have asked the High Court in the state of Kerala to throw out the murder charges against the two marines.
The marines were detained on Sunday and remanded in custody for two weeks as the murder investigation against them continues.
“As far as the law point is concerned,” Ms Kaur said, “they have their interpretations and we have our interpretations.
Mr Mistura expressed his regret over the two Indian fishermen’s deaths, but said there were legal points that needed to be clarified, including the exact position of the ship when the two men died.
“We do acknowledge that two Indian citizens died… and we are terribly sad. The second one is that is that the incident took place in international waters and at the same time the investigations will assert the exact position,” he said.
Italy insists that its personnel cannot be charged under Indian law. It says the marines have immunity as the tanker was flying an Italian flag and was in international waters when the incident happened.
The marines have been identified as Massimiliano Latorre and Salvatore Girone.