The north Caucasus is home to many impoverished and mainly Muslim mountain tribes who have periodically rebelled against Moscow's rule.
In Nazran, the biggest city in the Ingushetia region, four people were killed on Friday in an explosion that destroyed a grocery store, emergency services said.
Police said they suspected an accidental gas blast, but a local interior ministry official said the explosion was deliberate.
The destroyed building housed a liquor shop and the owner had previously received threats from armed groups who demanded he stop selling alcohol, the official said.
"There was a blast and black smoke pouring out," Ruslan, a 39-year-old Nazran resident who was passing the building at the time of the incident, said.
"People were running away in panic... some were covered in blood."
In neighbouring Chechnya late on Thursday, at least 25 armed men raided the village of Benoi-Vedeno, killing three locals and setting several houses on fire, Russian news agencies quoted officials as saying.
An internet site with ties to the separatist movement said the men had killed 11 armed people linked to Ramzan Kadyrov, Chechnya's pro-Moscow president.
In Dagestan, a remote-controlled bomb killed a jogger in a park in the capital, Makhachkala, local police said.