MOSCOW - A loyalist to Prime Minister Vladimir V. Putin who served as the speaker of Russia's parliament resigned Wednesday. The move appeared to be part of the government's effort to stem public anger over alleged fraud in this month's parliamentary election.

Boris Gryzlov had served as speaker of the State Duma for eight years and helped make it a reliable rubber stamp of Putin's decisions.

Putin has ruled Russia for nearly 12 years as president, then prime minister. He is now campaigning to reclaim the presidency in March.

However, Putin's authority has been hurt by the Dec. 4 parliamentary election, which saw his United Russia party lose about 20 percent of its seats and barely retain its majority. Reports of widespread fraud in the voting led to antigovernment demonstrations across Russia last weekend, the largest the nation had seen since its Communist days.

Activists have vowed to keep the pressure on Russia's leadership, and on Wednesday the city of Moscow gave permission for three protests this month - one for up to 10,000 people Saturday, and two on Dec. 24 that can have up to 60,000 people total.

The U.S. government said Wednesday it hoped the tolerance of protests was a sign of progress in Russia. "We were greatly encouraged to see these rights and responsibilities carried out so well," said Assistant Secretary of State Philip Gordon.

Putin has promised a government reshuffle, and President Dmitry A. Medvedev said their United Russia should share senior positions in parliament with other parties.

The dour Gryzlov, who was chairman of United Russia and the speaker of the State Duma, said Wednesday he would not seek the speaker's job but would keep his party post.

Putin is the leader of United Russia but not a member of it, in a thinly veiled attempt to maintain his distance from the increasingly unpopular party, which has been dubbed the "party of crooks and thieves."

Gryzlov, who was evidently asked to step down, had become an emblematic figure in Putin's "managed democracy" system, which envisaged tight control over political life. Gryzlov's famous statement that "parliament isn't a place for discussion" reflected United Russia's domination of parliament and its marginalization of opposition forces.

Valery Khomyakov, the head of the Council for National Strategy think tank, said Gryzlov's lack of charisma made him a liability.