"A police reconnaissance group clashed with a gang of about 10 people in a forest at around 3:30 p.m. Moscow time [11:30 GMT] on Sunday. A deputy commander was killed and a serviceman sustained a severe injury," the official told RIA Novosti.
After the gang members evaded arrest, they were pursued to the Shali district where another shootout occurred 45 minutes later. A dug-out shelter used by the gang was discovered and destroyed in a nearby forest.
In a separate incident, a group of unknown offenders set fire to the administration building in Chechnya's Achkhoi-Martan district late on Sunday. An investigation is underway.
In neighboring Daghestan, two vehicles of a mobile police unit came under a fire at around 4:00 a.m. Moscow time [0:00 GMT] on Monday.
No casualties have been reported, although one of the cars was damaged. A search is being conducted.
Chechnya, a mountainous Russian republic in the Russian North Caucasus, saw two separatist wars in the 1990s-early 2000s. Thousands of people were killed and the republic's capital, Grozny, was almost completely destroyed.
Although the active phase of the war is over, sporadic clashes with militants and terrorist attacks are common in the troubled republic, as well as in adjacent republics such as Ingushetia and Daghestan.
Since becoming president of Chechnya in February 2007, Ramzan Kadyrov has overseen a period of relative calm in the republic, despite continuing allegations by human rights groups of torture and intimidation by local security forces.