The gunfight broke out late Saturday evening after security forces cordoned off the house.
He asserted his force was as competent as the CBI to probe the Kathua rape and murder case.
The exact number of terrorists is not known but as per initial calls received at PCR Jammu four to five terrorists were involved.
Bhopal Mukhiya of JAK Rifles, who is posted at Uri, was taken into custody after two hand grenades were recovered from his possession during search at the main gate of the airport
The attack by the LeT to free "hardcore" Lashkar-e-Tayiba terrorist Mohammed Naveed Jhatt took place around 11.35 am inside the busy SMHS hospital complex in a high security area of Jammu and Kashmir's summer capital.
The suspect is believed to have already arrived in the valley.
Jammu and Kashmir Director General of Police S P Vaid on Friday lauded the restraint shown by the Central Reserve Police Force jawans who were heckled by some youths in Budgham on Sunday, saying "any armed force in the world would have retaliated with force".
Jaish-e-Mohammad, the Pakistan-based terror outfit, has claimed responsibility for the attack.
Police have filed a case against the army personnel, an official said, adding that records kept at a police station were also damaged.
The martyred policemen were identified as Constable Ishfaq Ahmad Mir, Constable Javaid Ahmad Bhat, Constable Mohammad Iqbal Mir and SPO Adil Manzoor Bhat.
The bodies of two terrorists had been recovered on Sunday.
Jammu and Kashmir Chief Minister Mehbooba Mufti expressed anguish over the loss of lives and stressed the need for peace "if we want to save the people of the state".
Constable Mazoor Ahmed Niak came forward on two occasions after senior officers decided to bring down the house at Reshipora from which the two militants had continued firing on the police, army and the Central Reserve Police Force.
Army sources said the CoI has been given one month's time to complete the probe.
Their special skills of carrying out house intervention and hostage rescue can act as 'clincher' during a terror siege, the official said.
'Local support is very important, without it the terror attack couldn't have taken place.' 'Explosives were secured, the IED was manufactured, the boy was brainwashed and converted into a suicide bomber... it takes a lot of planning and hard work.'
The officer claimed 88 Kashmiri youths joined militancy in 2016.
The college student, a goalkeeper for his local team in Anantnag in south Kashmir, is believed to have turned to militancy after a close friend was killed in an encounter.
The cash transactions have been stopped at the branches belonging to the Jammu and Kashmir Bank and Ellaquai Dehati Bank.
Chief Minister Mehbooba Mufti said she was deeply distressed by the killing of 'civilians' in 'crossfire'.
Restrictions have been imposed in five police station areas of Srinagar, a police official said.
The support for the eight-year-old girl was growing with politicians, cutting across party lines, seeking justice for her.
The slain armymen are Sepoy Ilayaraja P, from TN, and Sepoy Gawai Sumedh Waman, from Maha.
Three other terrorists, believed to be severely injured during the gunfight, managed to escape.
The incident took place at Bhatindi on Saturday morning when the man, hailing from Mendhar in Poonch district, drove at a high speed and banged his car against the main gate, they said.
The number is an all time high for the state with south Kashmir emerging as one of the main hubs, providing cadres to terrorist groups.
The army had to had to aim at the crowd when jawans claimed to have been fired upon from the other side.
Chief Minister Mehbooba Mufti warned that there could be a backlash if the force loses patience.
Using phones and computers to spread rumours, jihadis are waging a new, unconventional war.
Evacuation of people from the family quarters is in progress.