The two soldiers were killed on Monday in the mountains of southern Chechnya where most of the fighters are based. Similar attacks struck the capital, Grozny, where the pro-Russian policemen were seized, said the military sources.
One of the policemen was taken from his home and another grabbed out of his car while he was on patrol on the war-ravaged capital.
As violence raged on in the Caucasus republic a decade since the start of the first Russian war, Moscow news reports said that three men were also found dead in Grozny over the weekend while a teenager was killed in a blast in the southern mountains.
Russia first invaded Chechnya in December 1994 amid its claims for independence and refusal to bow to Moscow‘s rule. Russia lost the 18-month war that ended in a truce and a humiliating withdrawal of its forces.
Moscow re-launched the war in October 1999 after a wave of apartment block bombings in Russia that killed hundreds and were blamed by separatists on Russian security agents and by Moscow on separatists.
Russian President Vladimir Putin has refused to negotiate with the separatists, introducing his own government and constitution in Chechnya that cements its status as a part of Russia.