Emerging from over an hour-long closed-door meeting, Chandy told reporters that the incident took place in international waters and sought to raise the issue of compensation for the families of the victims.
But the chief minister said that the fishermen were killed in a "brutal manner" and "we did not discuss" the compensation issue.
The Italian side wanted to meet the relatives of the fishermen but were told that the situation is "not right" for it, Chandy said. Mistura said that the discussions were "fruitful".
"We have full fail in the judiciary... and we hope that something would come up in coming days," the Italian Minister said.
The Chief Minister quoted the Italian minister as saying that the same could happen to Indian military personnel in other parts of the world. According to Chandy, Mitsura said that the guards of the ship opened fire to protect the vessel.
Earlier, Chandy said in Thiruvanathapuram that his government would go ahead with prosecution of the two Italian naval guards who allegedly killed the Indian fishermen off Kollam coast, saying "it is the right and power of the state".