Smoke rises outside the airport after a bomb is defused
A spokesperson for India's Border Security Force said that four militants opened fire while driving towards the main gate of a military airport south of the summer capital, Srinagar.
Border guards manning the airbase returned the fire, killing all four militants.
"We foiled the attack," the Indian army spokesperson said.
Lashkar-e-Taiba, which sometimes releases details of its operations from Pakistan, said six Indian soldiers were killed in the attack.
Reports say security has been tightened around the airport.
India blames Pakistan for fomenting the Kashmir insurgency but Islamabad says it only offers moral and diplomatic support.
Responding to the attack, Indian Prime Minister Atal Bihari Vajpayee said: "I feel as if there is no point in talking to Pakistan.
"We have not closed all our doors, but as long as cross-border terrorism continues, we shall not have any talks with [Pakistan]," Mr Vajpayee told reporters in Lucknow.
Nuclear rivals India and Pakistan are due to hold talks at the forthcoming meeting of the United Nations General Assembly.
Mr Vajpayee's comments appear to put those talks in doubt.
Sharp rhetoric
In an apparent response, Pakistani leader Pervez Musharraf warned India not to threaten his country.
"India wants to take political advantage of the Afghanistan turmoil," General Musharraf said in an interview broadcast on Pakistan state television.
India has said it will deal ruthlessly with any militants who tried to infiltrate into Indian-administered Kashmir and blamed Pakistan for encouraging the violence.
But General Musharraf warned against any Indian move to cross the Line of Control and attack Pakistani-controlled Kashmir.
"They should never attempt it," he said. "They will be paid back in the same coin."
Tension has built up along the LoC, which separates Indian and Pakistani forces in Kashmir, over the past week.
Last Monday India launched attacks on Pakistani positions across the LoC, saying it was preventing militants from crossing into Indian-administered Kashmir.
It coincided with a visit by US Secretary of State Colin Powell to the region, who tried to calm the two sides.
On Monday, an Indian army lieutenant was killed and two soldiers wounded in Pakistani firing across the LoC.
Lieutenant Anup Kumar died of shrapnel wounds after Pakistani soldiers fired mortars on Indian positions overnight, the Indian army said.
"Heavy exchange of 60mm and 82mm mortar and heavy calibre weapon fire was continuing in the area until Monday morning," an army official said.