"You must hand in reports on the measures you have taken on all complaints filed during the election campaign to the Interior Ministry by Dec. 15," Interior Minister Rashid Nurgaliyev told a ministry meeting in Moscow.
Nurgaliyev said 156 complaints of voting irregularities have been received on a special police hotline, RIA Novosti reported.
Nurgaliyev made his comments at a ministry meeting in Moscow the day ahead of a major rally expected to take place in the Russian capital's central square, protesting last weekend's parliamentary election results.
About 33,000 people have registered on Facebook their intentions to take part in the demonstration, which could turn into the largest rally since the fall of the Soviet Union in 1991.
Prime Minister Vladimir Putin blamed U.S. Secretary of State Hillary Clinton for protests against him. Putin said Clinton questioned the fairness of the election with minimal and skewed information.
Putin's party won the largest share of parliamentary seats in the election, with an unofficial count of 49.3 percent of the vote. But critics allege as much as half the total was gained through fraud, which has been widely reported by individual observers and the country's only independent voting watchdog, the Golos Association.
Golos, which received U.S. and European Union funding after being denied funding from Moscow, reported about 7,400 alleged violations early Friday, including ballot-box stuffing and the use of government resources for the benefit of Putin's party, a United Press International review indicated.
The non-governmental organization's Web site fell to Moscow-supported hacker attacks this week, The Wall Street Journal reported.
"I looked at the first reaction of our American partners (to the elections)," Putin told a televised meeting with supporters Thursday. "The first thing that the secretary of state did was characterize them as dishonest and unfair.
"She set the tone, gave the signal, and the signal was heard by certain activists. They heard this signal and, with the help of the State Department, they started active work."
He said the West spends "hundreds of millions of dollars" to influence Russia's election system.
Clinton, in Brussels, said she expressed justifiable, substantiated concerns about the voting.
"Human rights is part of who we are," she said. "And we expressed concerns that we thought were well-founded about the conduct of the elections."
She said other nations raised concerns too.
Mikhail Gorbachev, the last Soviet leader, called on Moscow Wednesday to annul the election results and hold a new vote.
Street protests in Moscow -- one of several cities where protests occurred -- resulted in about 1,000 arrests, The Moscow Times reported. Several opposition leaders received 15-day prison sentences.
The Kremlin has about 50,000 police and 2,000 paramilitary troops on Moscow's streets to quell demonstrations.
Opposition organizers plan a 4-hour demonstration Saturday, following the Russian election commission's announcement of the official election results.
Rallies were planned in more than 95 other Russian cities, as well as in New York, London, Paris, Kiev, Geneva, Stockholm and cities in more than 10 other countries.
The Moscow demonstration's location, originally set for Revolution Square outside the Kremlin, was disallowed by Moscow city authorities, who said they approved a rally of only 300 people.
The city Thursday told the organizing Solidarnost, or Solidarity -- the liberal democratic political movement named for the early 1980s Polish opposition movement -- it wanted the demonstration moved to Bolotnaya Ploshchad, or Marsh Square, across the Moskva River from the Kremlin.