One of the Russian serviceman died and another eight were injured as federal outposts came under fire 16 times in the past 24 hours, an official in the Kremlin-backed Chechen administration said on condition of anonymity on Friday.
An armoured personnel carrier blew up on a land mine, killing two servicemen and wounding two, the official said.
Another military vehicle exploded on a land mine in the Chechen capital of Grozny on Thursday night, leaving one soldier dead and four more wounded.
Another soldier died after carelessly handling his gun, the official said.
Russian forces left Chechnya in 1996 after a disastrous 20-month war against separatists ended in a stalemate, which left the republic de-facto independent but with a weak central government.
Russian troops rolled back in again in September 1999, after Chechnya-based fighters launched incursions into neighbouring Dagestan.
Meanwhile, Chechen officials told the Interfax news agency that 47 Chechens residents have been abducted so far this year. Deputy Prime Minister Movsur Khamidov said that 581 people were abducted last year and 127 went missing.
"The rate of abductions has been decreasing lately, and more significance is being attached to the problem," he was quoted as saying. "The screws are being tightened to put an end to the abductions."
Human rights groups have blamed Russian troops, Chechen fighters and a security service run by pro-Moscow Chechen President Akhmad Kadyrov's son in connection with the abductions.
The Memorial human rights group said on Friday that it had recorded 33 abductions in Chechnya in January.
According to its information, 14 of those seized were released and one was found dead, Interfax reported.