The country's police force faces a "series of important tasks," including "more effective defense of citizens' freedoms and rights, their property and a decisive battle against corruption," Medvedev said in a statement posted on the Kremlin web site.
Public opinion polls consistently show police as one of the country's least-trusted institutions.
Of 1,500 people polled by the pro-government Public Opinion Foundation, 54 percent said they believe that police work "badly" or "very badly," while 32 percent said police worked "satisfactorily."
Just 7 percent said police work "well" or "perfectly," while the remaining 7 percent had difficulty answering, according to the poll, which was released last week and had a margin of error of 3.2 percentage points.
Moscow city police chief Vladimir Pronin, meanwhile, said in an interview published Monday in Komsomolskaya Pravda that the city police force would cut its staff by 15 percent.
Pronin said the biggest cuts would be made in the city traffic police in a move that he said could help alleviate Moscow's traffic woes.
"Fewer traffic officers means fewer traffic jams," Pronin told KP.
Pronin acknowledged that "unfortunately, there is corruption in the police" and said the base salary for police officers could be raised to 21,000 rubles ($780) per month in an attempt to reduce incidences of bribery. "It is necessary to solve this problem using economic levers," Pronin told the newspaper.
A city police spokesman said the staff cuts were still under consideration and that if they are carried out they would take place no earlier than December.
Those officers made redundant would most likely be moved to other state agencies, the spokesman said. "We have vacancies in other agencies where they could be used," he said.
Interior Minister Rashid Nurgaliyev on Monday praised police for cracking down on crime, saying registered crimes were down 11 percent through the first nine months of this year compared to the same period last year, Interfax reported. Violent crimes were down 12.3 percent and street crimes down 5 percent, Nurgaliyev said.
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