The assailants attacked a checkpoint in the eastern region of Gudermes with guns and small grenade launchers late on Monday night, causing the first recorded casualties since separatist rebels announced a unilateral ceasefire last week.
Also, on Tuesday morning outside the capital, Grozny, three Russian bomb-disposal experts were wounded when an explosive device went off as they were trying to defuse it, the official said.
In a statement posted on the rebel website kazkavcenter.com, the separatists said they would observe a ceasefire until 22 February as a "sign of goodwill" - the first time they have halted hostilities in the more than five years of the guerrilla war.
The statement was signed by Chechen rebel leader Shamil Basayev, considered a hardliner who does not recognise the authority of Chechen leader Aslan Maskhadov and who has masterminded a series of attacks on Russian civilians.
In a newspaper interview published on Monday, Maskhadov urged Moscow to open peace talks in response to the rebel truce, but the Kremlin immediately rejected the initiative, saying it did not negotiate with "terrorists".
Rebel leader alive
Basayev appeared on the website on Tuesday to vow unstinting resistance.
Separatist leader Maskhadov (R)
called on Moscow to open talks
The fighter dug a knife into his artificial right leg several times in Kazkavcenter footage, dated Sunday, as he vowed that his followers would keep on fighting the Russians even after his death.
"I do not understand how the stronger side, and the Chechen side is the stronger side, can simply end a war," Basayev said.
"Our whole people have been held hostage for six years."
Russian troops, which rolled into Chechnya in October 1999 in the second such conflict in a decade, have faced daily resistance, with the death toll among federal forces each day often reaching five or more.