The army says that its ready for more attacks
The Pakistan-based militant group Lashkar-e-Taiba says it was involved in a five-day gun battle with troops in Indian-administered Kashmir.
At least 25 people died in fighting at Kupwara, including eight soldiers.
Lashkar-e-Taiba is the group which India holds responsible for the armed attacks in Mumbai last November in which more than 170 people died.
The army says the militants were well trained and equipped and had the backing of agencies in Pakistan.
"The maps and communication equipment [recovered from dead gunmen] indicates that [Pakistani] state and security forces' assistance was there as such material is not available in the civil domain," Brig Gurmeet Singh told a press conference in Srinagar on Wednesday.
"The majority of the militants have been killed and those left, if any, will also be eliminated."
He said most of the barbed-wire fence along the Line of Control (LoC) which divides Indian- and Pakistani-administered Kashmir is now buried under snow, which was probably how the militants managed to infiltrate into Indian territory.
The brigadier said his troops were "militarily prepared" to deal with the threat posed by between 300 to 400 militants currently operating in the Kashmir valley.
For five days Indian troops battled against the militants in thick forests, close to the LoC.
A spokesman for Lashkar-e-Taiba (LeT) who contacted local journalists said only 10 of the group's fighters had died - and the number of soldiers killed was far higher than officially admitted.
He said that the coming days would "prove costly" for Indian forces.
The BBC's Chris Morris in Delhi says that the army will be determined to prevent LeT or any other militant group from disrupting general elections in Indian-administered Kashmir when polling begins next month.
State elections held at the end of last year were much more peaceful than many people had expected and the overall level of violence in Kashmir is far lower than it was a decade ago.
But our correspondent says that the LeT wants to send a message that its violent struggle for Kashmir is not over.
The army says that militants receive support from Pakistan
Many of its leaders have been taken into custody in Pakistan in the wake of last year's attacks in Mumbai.
But India alleges that the group still receives support from military and intelligence agencies in Pakistan.
Delhi believes a large number of Islamic militants are waiting on the Pakistani side of the LoC for the chance to infiltrate into Indian territory.
Defence spokesman Col JS Brar said that the fighting broke out in the higher reaches of the Shamsabari range on Friday morning after troops launched an operation to flush out the militants.