Pakistan said the shooting was unprovoked, while the Indian military said its troops responded to fire from soldiers across the frontier.
The tit-for-tat fighting threatens to reverse recent progress Pakistan and India have made in improving their historically antagonistic relationship. The two countries have fought three major wars since they achieved independence from British India in 1947, two of them over Kashmir.
The relationship reached a recent low point in 2008 when Pakistani gunmen killed 166 people in the Indian city of Mumbai. It has improved significantly since then, and the two countries have taken steps to improve cross-border trade and ease travel restrictions. But key issues, including Kashmir, remain unresolved.
The mountainous region is divided between the two countries, but both claim the area in its entirety. A cease-fire over Kashmir has largely held for about a decade, despite periodic firing across the disputed border that sometimes causes casualties.
The danger from Thursday's violence is that it comes on the heels of two more serious incidents in which Pakistan and Indian accused each other of sending troops across the border and killing soldiers, the first such accusations since the cease-fire went into effect in 2003.
The Pakistani army said the latest incident occurred Thursday afternoon when Indian troops fired at a post in an area of Pakistan-held Kashmir called Battal, killing a soldier named Havildar Mohyuddin. Pakistan said the shooting was "unprovoked."
But the Indian military said its troops responded after Pakistani soldiers fired on their positions.
"Our troops retaliated and an intermittent exchange of gunfire is continuing," said Indian army spokesman Col. R.K. Palta. "It's yet another cease-fire violation by the Pakistani troops."
The most recent round of violence started Sunday, when Pakistan accused Indian troops of raiding an army post and killing one of its soldiers. India denied raiding the Pakistani post, and said Pakistani shelling had destroyed a home on its side of the frontier.
On Tuesday, India said Pakistani soldiers crossed the border and attacked an army patrol, killing two Indian soldiers and decapitating one of them. Pakistan has denied the allegations.
Both countries summoned top diplomats from the other side to protest the attacks, and Pakistan said it wants U.N. military observers in Kashmir to investigate the incidents.
India on Thursday rejected the proposal to go to the U.N.
"We are certainly not going to agree to internationalize the issue or allow the U.N. to hold an inquiry," Indian Finance Minister P. Chidambaram told reporters.
Amid the rancour, there have also been attempts to tamp down tension over the violence.
Pakistani Foreign Minister Hina Rabbani Khar said Thursday that she hoped the recent incidents would not derail the process of improving relations between the two countries. She told reporters that she wants to continue down the track of "trust building" and "normalizing the region, which has been very unstable because of irresponsible actions and statements."
Associated Press writers Asif Shahzad in Islamabad, Tim Sullivan in New Delhi, India, and Aijaz Hussain in Srinagar, India, contributed to this report.Suggest a correction