The shootings in Bangargund village in northern Kupwara district prompted several thousand people to take to the streets, demanding punishment for the troops.
The soldiers fired on the youths who had left wedding celebrations that had gone into the early hours of Sunday.
The youths had ignored army restrictions on people going outside after dark, police said.
The area is labelled "highly sensitive" by the authorities, as they say it is used as a transit route by separatists sneaking in from Pakistan-administered Kashmir to battle New Delhi's rule in Indian Kashmir.
"The four were asked to stop but instead they started running away, prompting troops to open fire," army spokesman Vijay Batra said, expressing deep regret over the shootings.
He said the four youths were shot as they emerged from a wooded area and were mistaken for separatists.
Indian troops battling the separatist movement are often accused of human rights violations - including the shooting of innocent civilians - by rights groups and separatists.
The authorities say they investigate all complaints and punish those found guilty of abuses.
India says it investigates all
complaints of killing civilians
A police officer in Bangargund said the shootings triggered a demonstration in the village in which several thousand people, including women and children, held a protest demanding action against the soldiers involved.
India says there has been a "sudden spurt" in incursions from the Pakistani side of the disputed region by guerrillas over the past few weeks since snow blocking Himalayan mountain passes began melting.
However, it says the rise in incursions will not disrupt the peace dialogue between India and Pakistan that was formally launched in January 2004.
New Delhi accuses Pakistan of allowing separatists to train on territory under its control, an allegation Islamabad rejects.
More than 44,000 people have been killed in Indian Kashmir since the start of the separatist movement in 1989, officials say. Separatists say the toll is at least twice as high.