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The body of one of the soldiers was found "badly mutilated" in a forested area of the Himalayan territory on the side controlled by India, said Rajesh K. Kalia, spokesman for the Indian army's Northern Command.
The army said in a separate incident later in the day both sides shot at each other for more than an hour across the Line of Control (LoC) that divides Kashmir. After that more shots were fired over the line from Pakistan, with no more casualties or injuries, the army said.
A Pakistani army spokesman denied what he said were Indian allegations of "unprovoked firing".
He branded India's allegations "propaganda" to divert attention away from a clash along the line two days earlier in which Pakistan had said one of its soldiers was killed after an Indian incursion. India denied its troops crossed over.
India considers the entire region of snow-capped mountains and fertile valleys an integral part of its territory. Pakistan contests that and demands implementation of a 1948 U.N. Security Council resolution for a plebiscite to determine the wishes of the Kashmiri people.
India and Pakistan have fought three wars since their independence in 1947, two of them over Kashmir.
"The government of India considers the incident as a provocative action and we condemn it," the Defence Ministry said in a statement.
"The government will take up the incident with the Pakistan Government. We expect Islamabad to honour the ceasefire agreement strictly," the ministry said.
Firing and small skirmishes between the two countries are common along the LoC despite a ceasefire and slowly improving ties. The Indian army says eight of its soldiers were killed in 2012, in 75 incidents.
Away from the border, ties seem to be better. Pakistan's cricket team completed a two-week tour of India on Sunday, the first time it has visited in five years.
Kalia said Tuesday's "intrusion" about 600 metres across the LoC in Mendhar - about 220 km (140 miles) north of the Indian city of Jammu - marked "a significant escalation ... of ceasefire violations and infiltration attempts supported by the Pakistan Army".
"Pakistan army troops, having taken advantage of thick fog and mist in the forested area, were moving towards (their) own posts when an alert area domination patrol spotted and engaged the intruders," he said.
"The firefight between Pakistan and own troops continued for approximately half an hour, after which the intruders retreated back towards their side of the Line of Control."
He said India would take up the issue with Pakistan at a military flag meeting and also at a diplomatic level.
In 1999, Pakistan-backed Islamist infiltrators occupied the Kargil heights in the north of Indian Kashmir, and India lost hundreds of troops before re-occupying the mountains after bitter fighting that almost triggered a fourth war.
Indian military officials say the frequency of cross-border clashes has increased in recent weeks, with at least half a dozen ceasefire violations over the past week alone.
"I would say generally the picture has been a bit bleak," said Uday Bhaskar, an Indian military commentator and former director of the Institute for Defence Studies and Analyses, referring to relations between India and Pakistan.
"This incident only reiterates a certain pattern as far as the bilateral relationship is concerned."
He cited an apparent slowdown in Islamabad's commitment to granting India most-favoured-nation trading status and a visit in December to India by an adviser to Pakistan's prime minister whose comments infuriated the Indian government.