Most of the victims in the Dagestani town of Kizlyar were policemen, a police official told the AFP news agency. Local police commander Vitaly Vedernikov is believed to be among the fatalities.
The first blast was set off as a police car drove out of a local interior ministry building.
The second explosion, about 20 minutes later, was detonated by a suicide bomber dressed in police uniform, according to Russian news agency Interfax.
The blasts come two days after female suicide bombers killed 39 in attacks on the Moscow metro which the authorities have linked to militants from the North Caucasus.
It cannot be ruled out that the same group was behind these latest attacks, Russian Prime Minister Vladimir Putin said on Wednesday.
"This is a crime against Russia," Putin told a special meeting of the Russian government, adding that the special services were doing all they could to find those responsible.