An explosion went off at the intersection of Mayakovskogo and Babushkina streets on Friday when a Ural army vehicle carrying troops was driving by.
It was reported earlier that three people were killed and nine injured in the blast. One soldier died at the scene and two civilians died later in the hospital.
Colonel Abdulmanat Musayev, head of the Dagestani Interior Ministry's press service, said in a shootout during the pursuit of suspects, a police captain and a teenage girl were injured.
Police pursued three suspected gunmen who fled the scene in a VAZ-21099 car. The suspects escaped after a shootout, abandoning their car.
Musayev said a powerful explosive device and a lot of scattered cartridges had been found in the abandoned car, which had a fake license plate.