The soldiers were searching for militants during a patrol when they were ambushed in the village of Hardu Buchoo, 30 kilometres (19 miles) southeast of Srinagar near the forested area of Tral, the spokesman said.
"The militants fired at the soldiers from outside the village, when the cordon was laid and three of our soldiers were killed," Lieutenant Colonel Ankur Vashist told AFP in Srinagar.
The militants fled into the forest and the army called in reinforcements, Vashist said. Another soldier was wounded in the ensuing gun battle with the militants, he said.
The bodies of the soldiers have not yet been retrieved, he added.
The ambush comes a day after government forces killed a top militant from outlawed group Lashkar-e-Taiba (LeT) in Srinagar during an early morning gun battle.
Indian Kashmir has been tense since the execution in February of a local man over a deadly 2001 attack on the national parliament in New Delhi.
Mohammed Afzal Guru was convicted over the attack, but he retained widespread support in Kashmir where many doubted his guilt.
Much of Kashmir has since been put under curfew repeatedly while protests and strikes have disrupted daily life.
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I think it is the time for Indian Government to think about to free all people of Kashmir to go wherever they want to go. (If someone wants to stay here he must welcome & not then most welcome) After all Kashmir is not for any particular religion.
Inna Lillahi wa inna ilaihi raji'un