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As investigators and residents gathered at the scene of the blast, a second bomber dressed as a policeman approached and set off explosives, killing the town's police chief among others, said Vyacheslav Gadzhiyev, another ministry spokesman.
Tatyana Batsina, who was working near the site when the blast occurred, told RIA Novosti she heard a loud bang and saw a cloud of smoke rising from behind a nearby school.
"It looked like in a nuclear explosion," she said. Around half an hour later, she heard another blast.
"Two cars driving past were also harmed in the explosion. A crowd gathered around the first explosion. Everyone wanted to see what had happened. Several ambulances arrived, then another blast rang out," she said.
Investigation official Nizami Radzhaboiv said bomb experts estimated the power of the first explosive device in Kizlyar was equivalent to up to 200 kg of TNT.
After the explosions, Russian Interior Minister Rashid Nurgaliyev ordered tighter security at public places in Dagestan.
Dagestani authorities had launched a criminal investigation over the two explosions, he said.
Medvedev ordered Dagestani authorities to provide all-round support for the families of the victims, as well as to provide all necessary assistance, including medical and financial, to the people injured.
Groups from the North Caucasus, which includes Dagestan and Chechen, were blamed for organizing the Moscow metro attack though no claims of responsibility have been made yet.
In January, a suicide bomber set off a car bomb at a police station in Makhachkala, the capital of Dagestan, killing six officers.