The army officer was shot dead after Wednesday's first meeting between the foreign ministers of the two countries in a year as part of a comprehensive peace dialogue.
"The fighting in Kupwara (north Kashmir) erupted when a group of heavily armed militants tried to infiltrate into our territory from the Pakistani part of Kashmir," Indian army spokesman J.S. Brar told AFP.
The clash, in which two Indian soldiers were also wounded, ended early Thursday after erupting the previous day. Indian soldiers were hunting for the militants.
India says it regularly intercepts militants sneaking into Indian Kashmir. Pakistan denies Indian allegations it helps the insurgents cross into Indian Kashmir.
The latest fighting came after Indian foreign minister S.M. Krishna and his Pakistani counterpart, Hina Rabbani Khar, outlined in New Delhi the countries' commitment to fight militancy, boost trade and sustain the peace process.
Krishna said ties were back "on the right track," while Khar spoke of a "mindset change" that had ushered in a "new era of cooperation".
Kashmir Chief Minister Omar Abdullah described the meeting as a "good step" but Kashmiri leader Syed Ali Geelani termed the outcome as "superficial" and urged the two sides to address "the core issue of Kashmir."
Among agreements concluded between the sides, the two countries said they would increase the frequency of trans-Kashmir bus service from fortnightly to weekly and strengthen telephone communications between the two sides.
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