News agencies said the Russian soldiers were killed when Chechen separatist fighters attacked a vehicle carrying troops through the southeastern region of Vedeno.
Russian military sources said their forces killed 17 separatists in a series of raids.
Russian news-agency Interfax quoted a senior Russian commander saying that four rebels had been killed in a forest near the western village of Samashki while another six were killed near the village of Shali.
Another seven rebels and two pro-Russian Chechen police officers were killed overnight in what authorities said was an aborted guerrilla attack on a village.
A Chechen police officer working for the republic’s pro-Russian administration was killed when separatist fighters attacked a checkpoint outside the provincial capital of Grozny.
Chechen fighters have been battling Russian forces in pursuit of their goal to secure Chechnya’s independence from Moscow.
Russian forces rolled back into Chechnya in 1999, tearing up an autonomy agreement for the breakaway republic reached by President Putin’s predecessor Boris Yeltsin and the man who was later elected to become the region’s president, Aslan Maskhadov.
In a bid to end the protracted war on its terms, the Kremlin has scheduled a presidential election for the province next October following the adoption of a new constitution that granted Chechnya the status of a republic within the Russian Federation.
Rights groups have also criticised the Russian plan for failing to include talks with the fighters, who have promised to step up attacks.