There were no independent estimates of Chechen casualties.
Four soldiers died and four others were wounded during 14 separate attacks on military positions around the tiny republic in Russia's North Caucasus mountain region on Friday, said the official in Chechnya's government.
Two members of the irregular Vostok battalion - made up of pro-Russian Chechens, but fighting under command of Russia's elite Main Intelligence Directorate, or GRU - died in fighting in the devastated capital Grozny. Three others were wounded.
In another part of the city, three Russian policemen were shot. In the southern town of Urus-Martan, another two policemen were wounded when their vehicle hit a landmine. Two soldiers were wounded in the mountainous area of Itum-Kale.
The casualties, which occurred within a period of 24 hours, were the latest in Russia's secretive war against separatists, despite official claims that the fighting is over.
Independent observers believe that about 20,000 Russian soldiers have died in the current conflict, which began in 1999, and in the previous war, fought between 1994 and 1996.
As many as 100,000 Chechens, mostly civilians, are estimated to have perished over the last decade, according to various independent accounts.
The official daily statement from the military headquarters for the North Caucasus region made no mention on Friday of any losses.