Five other security force officers were also injured in a separate clash in Chechnya on Thursday, Russia's Interfax news agency reported.
"A whole series of political murders and attempted murders are aimed at destabilising the situation in the Caucasus"
Dmitry Medvedev, Russia's president
Speaking after talks with Angela Merkel, the German chancellor, in the Russian city of Sochi, Medvedev said: "A whole series of political murders and attempted murders are aimed at destabilising the situation in the Caucasus."
Yunus-Bek Yevkurov, the president of the southern Russian republic of Ingushetia, survived an assassination attempt when a car bomb was detonated next to his convoy in the capital Nazran on June 22.
Referring to the attack in his remarks, Medvedev said: "I mean the murders of our rights defenders, I mean the attempted murder on the new president of Ingushetia."
The president said unspecified armed groups in the Caucasus were receiving support from "foreign sources" that he did not name.
He also called on Ramzan Kadyrov, the Moscow-backed Chechen leader, to find those responsible for the latest killings in the region.
"The president of Chechnya must do everything in his power to find and unmask these killers," he said.
Police blamed the bath house attack on groups who target women deemed to violate the moral standards of Islam and local clan codes.
They said Thursday's massacre, in the city of Buinaksk, was a deliberate attack on prostitutes.
The lastest killings are the most recent incidents in a sharp upturn in violence across the region.
|Sadulayeva, a Chechen woman who helped maimed children, was killed earlier this week
On Wednesday, a construction industry minister in Dagestan was shot dead in his heavily-guarded office.
Three human rights activists have also been killed in Chechnya in the past month, while the body of a local journalist in Dagestan was found earlier this week.
Zarema Sadulayeva, a Chechen woman who helped maimed children, and her husband were kidnapped and killed earlier this week.
Last month Natalia Estemirova, a prominent activist for the rights group Memorial, was abducted and killed.
Memorial and other human rights organisations have suspended their operations in the region as a result of the attacks.
The rising violence throughout Russia's North Caucasus is undermining the Kremlin's claims to be enforcing effective law and order in the region.
While large-scale fighting from the two wars that ravaged Chechnya since 1994 has ended, rebel fighters continue to mount hit-and-run attacks and skirmishes with Russian and Chechen security forces.
Bloodshed has surged in recent months and increasingly spilled into Chehnya's neighbours.
"Certainly, what is happening now is being heated up from the outside, beyond the Russian borders," Ali Magomedov, Dagestan's interior minister, was quoted as telling Interfax.
"There can be no other explanation. Dagestani people do not need to kill one another."
Merkel condemned the slaying of Sadulayeva and her husband as "absolutely unacceptable".