Russian President Dmitry Medvedev says accusations of fraud that led to large protests following Sunday's parliamentary elections should be investigated.

Mr. Medvedev said Thursday Russia's electoral system is not perfect. But he said he believes the results reflect the political preferences of Russian society and that political observers agree the elections were well organized.

President Medvedev called for Russians to stay calm during the investigation, and said protests are fine as long as they are conducted within the law.

Russian Prime Minister Vladimir Putin accused the U.S. of riling up the opposition following the elections. Mr. Putin's United Russia party won Sunday's vote, but with a considerably reduced parliamentary majority.

Secretary of State Hillary Clinton said Tuesday the elections were neither free nor fair.

Opposition organizers have scheduled four more major protests to be held in Moscow over the next 10 days, with the first set for Saturday near the Kremlin. Authorities have granted a permit for 300 people, but 23,000 have pledged to attend through Facebook and a Russian social networking site.

Opposition leaders oversaw three days of protests this week to express their frustration with the elections. International observers say Sunday's vote was marred by widespread allegations of ballot-box stuffing and other irregularities.

Former Soviet leader Mikhail Gorbachev has called for Russia's election to be annulled and a new vote held. He said the results do not reflect the will of the people.