At least four attackers and seven Indian soldiers have died so far.
An Indian official said two gunmen were still at large, contradicting reports that the base was secured on Saturday.
The attack is being seen as a blow to an apparent peace initiative launched just over a week ago.
Hopes for a thaw in relations were raised after Indian Prime Minister Narendra Modi paid an unexpected visit to his Pakistani counterpart, Nawaz Sharif.
Pakistan's foreign ministry and the US State Department have condemned the attack.
The attack 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 Saturday afternoon, police said the base had been secured.
However, fresh gunfire was reported on Sunday morning.
A senior government official, Home Secretary Rajiv Mehrishi, troops were battling at least two gunmen who had been cornered at the site.
At least one explosion - suspected to have been caused by a grenade - was heard on Sunday. Local news reports said a soldier from a commando unit had been killed while defusing explosives.
The identity of the attackers is not clear. Some Indian security officials suggested the Islamist militant group Jaish-e-Mohammed was to blame.
India says the group is backed by Pakistan, but Islamabad denies this.
In July seven people were killed in a similar attack when gunmen stormed a police station in nearby Gurdaspur district. The three attackers in Gurdaspur were killed after a 12-hour standoff with police.
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.
Fresh gunfire and a blast have been heard at an Indian air force base at Pathankot near the Pakistani border, as troops reportedly battle the remnants of a group that attacked the site.