In his petition, Kalia urged the global body to ensure full and independent investigation into the case and also to conduct inquiries into the matter and find out the people responsible for his son's death.
He termed his son's death as a war crime.
"We want that at least Pakistan should admit it and apologise that yes, our soldiers have done it and we will not be doing such things to any other soldier ever," Kalia said.
He had recently moved the Supreme Court seeking its direction to the government to raise his son's case at the International Court of Justice at Hague.
He alleged that his son was captured as a prisoner of war but was killed in a gruesome manner in violation of the Geneva Convention.
Capt Kalia and five other soldiers of his patrolling team were captured alive on May 15, 1999 by Pakistani troops and kept in captivity where they were tortured and their bodies mutilated. Their bodies were handed over to the Indian side later.
The army has promised full support to Kalia and his family.