Medvedev earlier sacked police Maj.-Gen. Viktor Ageyev, who headed the police department in Moscow's Southern Administrative District, where one of his senior officers, Tsaritsino district police chief Denis Yevsyukov, shot three people dead early on Monday.
Following a family quarrel Yevsyukov, 32, took a taxi to a supermarket in southern Moscow shortly after midnight on Monday, where he shot the driver dead, before walking into the store and killing two more people. Six people were wounded in the attack.
Pronin, who personally visited the scene of the crime and spoke to Yevsyukov hours after the killing spree, told Russian media that the killer had until then been considered a good officer with strong potential, having served 14 years on the force without complaints from colleagues.
After questioning him, Pronin said: "His eyes were like saucers - he was not aware of anything and remembered nothing of what had happened - he just cried."
Russian Interior Minister Rashid Nurgaliyev said on Tuesday in an interview with Russia's Vesti news channel that the ministry would provide support and assistance to all the victims and their families and would conduct inspections in Moscow police departments.