The army said a patrol party was targeted by landmines and firing by a group of unidentified armed personnel or militants who were trying to cross over.
The incident took place at 10 am on Sunday, when a team of the Maratha Light Infantry went to rescue a soldier, Vinod Kumar, who was injured in a landmine blast at the Pallanwalla sector near the Line of Control.
The landmine was allegedly planted by militants who ran towards a Pakistani post when Indian troops fired at them.
Pakistani troops allegedly opened fire and wounded three soldiers. One of them, Sepoy Bhikale Uttam Balu, later died.
The defence ministry said a search of the area revealed Pakistan-made landmines and other equipment that pointed to the involvement of militants and Pakistani soldiers from across the border.
There have been several infiltration bids this month by Pakistani militants along the Line of Control. On May 10, two militants were killed in the Poonch sector, where infiltrators had tried to enter earlier on May 3.
In 2013, 12 jawans were killed and 41 injured in the highest number of ceasefire violations - 149 - and firing by Pakistan troops along the India-Pakistan border.
Pakistan's Prime Minister Nawaz Sharif has expressed hope for good ties with the new BJP-led government to be helmed by Mr Modi.
Mr Sharif has reportedly cited his working relationship with Atal Bihari Vajpayee, the last prime minister to lead a BJP government, as a reason for his optimism.
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