According to the latest Russian media reports, at least three Chechens and one Ingush policemen were killed and more than a dozen wounded.
It was not immediately clear what sparked the clash. Initial reports said the clash began after the Chechens refused to identify themselves. Other reports suggest Ingush police opened fire without warning on the Chechens, who were returning home after a special operation across the border.
A spokesman for the Ingush interior ministry said the incident was a "fatal mistake."
Senior officials from both sides are at the site investigating the incident.
The aftermath of a December 2002 Chechen resistance attack on the main government building in Grozny (epa)