ISLAMABAD — Pakistani and Indian troops exchanged gunfire across the disputed Kashmir border early Sunday, leaving one Pakistani soldier dead in a relatively rare fatal confrontation between the two neighbors.

As usual, the rival armies, which have been engaged in a faceoff in Kashmir for decades, disagreed about who started the shooting or what happened next. Pakistan said Indian troops crossed the disputed boundary, known as the Line of Control, into Pakistani-controlled territory, where they attacked a remote outpost and wounded two soldiers, one of whom later died.