Officials said troops had been fired at by Chechen fighters 19 times during the past 24 hours, leaving four soldiers dead.
Another two soldiers died in a gunfight near the village of Gekhi.
One more soldier was killed and two others wounded when a landmine blew up a military car in Urus-Martan.
Authorities also discovered and defused a shrapnel-filled bomb left near a bus stop in the Chechen capital of Grozny.
Officials, meanwhile, confirmed that Friday's explosions on gas and oil pipelines in southern Russia had been carried out by the Chechen fighters.
The first of the two blasts struck on the Mozdok-Kazimagomed line, which pumps natural gas to Azerbaijan. The second struck the Baku-Novorossisk oil pipeline.
"Most likely it was a terrorist attack," Uvluby Erbolatov, a regional official in Dagestan, the southern Russian republic bordering Chechnya where the explosions occurred, said.
Chechen fighters have been battling Russian troops since 1999, seeking the republic's independence from Moscow.
It has been a bloody war, claiming thousands of lives on both sides with human rights groups accusing Russia of gross abuses. Chechen separatist politicians have charged Moscow with conducting a slow genocide.
Ramzan Kadyrov, the son of Kremlin-supported Chechen President Akhmad Kadyrov, has meanwhile predicted that the surrender of a key ally of separatist leader Aslan Maskhadov will weaken the Chechen fighters.
Federal authorities on Friday had announced that Shaa Trulayev, head of Maskhadov's bodyguard corps, had surrendered to Russian forces.
Maskhadov commanded the separatist fighters in the first of the past decade's two wars in Chechnya and was elected the republic's first president in January 1997.
His authority and control over resistance fighters in the current war has been weakened by strong senior commanders.