The encounter in the Kulgam district of Jammu and Kashmir entered the second day on Tuesday as security forces were engaged in a gunbattle with terrorists.
"The operation against terrorists in Kulgam has resumed this morning after a brief lull in firing overnight," an official said.
Two terrorists, including one believed to be a Pakistani national, and two soldiers were killed in the fierce encounter that started on Monday. An Army major was also injured in the operation.
The encounter erupted after security forces launched a search operation in the Gudar forest area of Kulgam based on specific intelligence about the presence of terrorists, who opened fire on the security forces.
During the operation, two soldiers, identified as Sub Perbhat Gaur and Lance Naik Narender Sindhu, and an Army major were injured in the gunfight, the officials said.
Gaur and Sindhu succumbed to their injuries while the officer's condition is stated to be stable.
A tweet by the Army's Kashmir-based Chinar Corps said that it "honours the supreme sacrifice of the bravehearts, Sub Perbhat Gaur and L/Nk Narender Sindhu, in line of duty for the nation. Their courage and dedication will forever inspire us".
Earlier, based on an intelligence input from Jammu and Kashmir police, a joint search operation was launched by the Army, CRPF and police in the Guddar forest of Kulgam.
Vigilant troops observed suspicious activity and were met with gunfire when they challenged the terrorists.
Initial reports indicate one of the neutralised terrorists was a local, while the second is believed to be a foreign militant with the code name 'Rehman Bhai'.
Director General of Police Nalin Prabhat visited the encounter site in Guddar, where he praised the joint operation led by the Army.