The United Jihad Council - a coalition of militant groups fighting Indian rule in Kashmir - claimed its "national highway squad" was responsible.
The attack on the Pathankot airbase near the border with Pakistan is seen as an attempt to derail recent peace moves by Pakistan and India.
Indian PM Narendra Modi has held a meeting to discuss the raid.
Five militants and seven Indian soldiers have so far been killed during three days of fighting.
The United Jihad Council was formed in 1994 to co-ordinate resources and plans to hit military targets in Indian Kashmir among more than a dozen groups based in Pakistani-administered Kashmir. Those groups were widely seen as being brought together by Pakistan's ISI intelligence agency.
The UJC is led by Mohammad Salahuddin, the leader of the pro-Pakistan Hezbul Mujahideen group, the largest in the alliance. The leadership of most of these groups is based in Pakistan, and they have been largely dormant since the 2003 ceasefire on the Line of Control (LoC), the de facto boundary dividing Kashmir.
So the claim by the UJC to have carried out this latest attack is likely to strengthen the view that it was authorised by the Pakistani army to undermine Mr Modi's recent peace overtures to Pakistan's civilian government. The Pakistani military has been accused of sabotaging the civilian-led normalisation process with India on several occasions in the past.
The UJC could also be trying to remain relevant even after India strengthened the LoC to stop infiltration of militants from the Pakistani side.
Over the weekend some Indian security officials suggested the Pakistan-based Islamist militant group Jaish-e-Mohammed was to blame. India says the group is backed by Pakistan, but Islamabad denies this.
As the gun battle continued between Indian troops and militants at Pathankot, Indian TV stations reported that a loud explosion was heard at the base.
All roads leading to the base have been closed.
On Monday evening, a senior security official told a press conference that all families living on the base were safe and "all strategic assets [helicopters, aircraft and other military hardware] were secured".
Maj-Gen Dushyant Singh, from India's elite National Security Guard, said it would take a "long time" to declare the base completely secure, because of its size and geography.
Meanwhile, police in Punjab's Mohali district said they had arrested three men with illegal arms and recovered a Pakistani "SIM card" from them. It is not yet clear whether the men had any connection with the attack, police said.
The Pathankot assault started before dawn on Saturday, when a group of gunmen - wearing Indian army uniforms - entered the residential quarters on the base.
Hours of heavy gunfire followed and a helicopter was seen firing at the facility on Sunday.
The attack is being seen as a blow to an apparent Indo-Pakistani peace initiative launched just days ago.
Hopes for a thaw in relations were raised after Mr Modi paid an unexpected visit to his Pakistani counterpart, Nawaz Sharif.
Pakistan's foreign ministry and the US state department have condemned the attack.
Pathankot air force base is about 430km (270 miles) north of the Indian capital, Delhi, and is on the road linking Indian-administered Kashmir with the rest of the country.
Indian-administered Kashmir has seen a long-running insurgency against rule from Delhi, and Kashmir has been a flashpoint in relations between Pakistan and India for nearly 70 years since independence.
A strategic location
- The Pathankot air force base extends over about 2,000 acres, including some areas covered with tall vegetation.
- The base's commanding officer Lt-Col JS Dhamoon has described it as a "mini-city". It includes homes and a school for the children of air force personnel.
- Pathankot is home to a fleet of MiG-21 fighter jets and Mi-25 and Mi-35 attack helicopters, along with other military hardware.
- The base and the state of Punjab as a whole has "probably the highest concentration of military personnel in India because it's so close to the border with Pakistan," analyst Rahul Bedi from Jane's Information Group told AP.
- It occupies a highly strategic position on the main highway connecting Kashmir with the rest of the country. It is also very close - about 35km - to the border with Pakistan.
