KANDAHAR, Afghanistan — NATO and Afghan forces are investigating a claim by the Afghan police that American soldiers fired on them for no reason, killing four officers and wounding two others, and inflaming tensions in southern Afghanistan’s Arghandab Valley, where security gains brought by the surge of American troops remain brittle.

While there have been dozens of cases of Afghan soldiers firing on members of the NATO-led military coalition, reports of NATO soldiers firing on their Afghan counterparts are rare. American and NATO officials have yet to release details of the shooting, which took place on Tuesday evening at a police checkpoint outside Combat Outpost Tynes, a small base in the volatile Arghandab district of Kandahar Province.

By Thursday, word of the shooting was stirring anger in the area, where some residents had vowed to stop helping the Americans if the soldiers responsible were not brought to justice.

In bedside interviews at a military hospital in Kandahar on Thursday, the two wounded officers gave nearly identical accounts of the shooting. The officers, one the police commander, were interviewed separately.