Fighter jets and helicopters hit targets during day and night.
The holed-up militants have so far ignored appeals to surrender.
Fayaz Ahmad Dar, shot himself with his service rifle inside battalion headquarters of Central Reserve Police Force at Chrar-e-Sharief, a police spokesman said.
The police spokesman said the LeT terrorist has been identified as Sajad Ahmad Shah, a resident of Gund in Chogul area in north Kashmir's Kupwara district.
One of the slain militants were identified as Wasim, a Pakistani national and self-styled district commander of JeM.
India handed over the dossier to the acting high commissioner of Pakistan in New Delhi on February 27 with specific details of Pakistan-based terror group Jaish-e-Mohammed's complicity in the Pulwama attack that killed 40 Central Reserve Police Force personnel on February 14 and the presence of JeM terror camps and its leadership in Pakistan.
The anti-terrorist operation was still in progress.
A policeman was critically injured on Monday after a suspected terrorist attacked him with a knife at Pampore in Pulwama district of Jammu and Kashmir, the police said.
Following reports of firing at Gulshanpora area, the forces had laid an ambush in nearby Seer Jagir area of Tral on Tuesday evening.
The inquiry was ordered in view of allegations against the security forces and protests by the public, he said.
Police and security forces have rushed to the spot.
'Some within India are terming Imran a statesman for sending back our pilot'
A top Lashker-e-Toiba militant involved in last year's serial blasts in Uttar Pradesh was killed along with another ultra of the outfit in an encounter with police in Pulwama district on Friday, a senior police official said. The self-styled district commander of LeT, Abdul Rahman of Pakistan alias Rehman Bhai and a local militant Moin Ahmed Mir, were killed in the gunfight with Jammu and Kashmir police personnel at Nikloora-Aglar village.
In a joint operation, police, Rashtriya Rifles and Central Reserve Police Force arrested LeT militant Mohammad Ashraf Sheikh alias Moulvi from his village at Rampora in Pulwama district, a police spokesman said.
After hearing the news of his death, hundreds of Muslims gathered at his residence to perform his last rites.
Fresh clashes broke out between protesters and security forces in Kashmir, even as Union Home Minister Rajnath Singh is set to visit the Valley on Saturday.
What the election demonstrated is that the BJP has a stranglehold on most of the Hindu votes in the Union territory, observes David Devadas.
Security forces faced stone-pelting during the operation but exercised maximum restraint.
According to the order, all security and vehicles provided to the separatists will stand withdrawn by Sunday evening. No security forces or cover will be provided, under any pretext, to them or any other separatists. If they have any other facilities provided by the government, they are to be withdrawn forthwith.
Violent clashes were witnessed at two places in Kashmir on Friday, with stone-pelting mobs attacking security personnel who retaliated by lobbing teargas shells, officials said.
Removal of this status means India can now enhance customs duties to any level on goods coming from Pakistan.
A defence spokesman clarified that the civilian died when militants, escaping after attacking an army column, opened fire.
The gun battle broke out at Imamsahib in Shopian, around 60 km from Srinagar, when troops engaged in combing operation were fired upon, the sources said.
Hardline Hurriyat Conference Chairman Syed Ali Shah Geelani has stoked a controversy by paying tributes to 2 militants who were killed in an encounter in Tral area of Kashmir, in which an army commander and a policeman died.
The encounter broke out when troops confronted a group of militants trying to sneak into the valley from across the border.
Police said the injured have been taken to various hospitals in Srinagar.
Unidentified gunmen abducted a Bharat Sanchar Nigam Limited official from his residence in Pulwama district of Jammu and Kashmir, officials said on Tuesday.
In another incident, militants in Pulwama district shot at a man on Sunday night.
Kashmir witnessed a spontaneous shutdown to mourn the killing of Hizb commander Sabzar Bhat in an encounter with security forces in Tral area of south Kashmir's Pulwama district on Saturday. Soon after the news of Sabzar's killing spreads shopkeepers lowered their shutters and public transport disappeared from the roads. Students took to streets in several areas of Ganderbal district of central Kashmir, where a spontaneous shutdown is being observed in the district.
Two top militants of Harkat-ul-Mujahideen were shot dead by security forces in Pulwama district on Saturday morning, a defence spokesman said.
Police said two army soldiers of 42 Rashtriya Rifles who were injured in the militant attack were evacuated to a hospital for treatment.
The government has termed as "highly regrettable" the Budgam incident in Kashmir valley in which two civilians were killed and as many injured in Army firing and said a fair inquiry will be held and action taken against those found guilty.
A youth died in clashes between stone-pelters and security personnel near the encounter site.
5 ultras killed, 4 arrested, 60 kg explosives seized in J&K
Shazia, who had suffered multiple splinter injuries, died on Saturday evening.
In another incident, militants chopped off the hands of a man in Tral Area in Pulwama district, 30 km from Srinagar.