The opposition said some 2 million supporters thumb-printed the petition.
Official election results extended Hun Sen's 28-year rule and gave his party 68 seats in Parliament, compared to 55 for the opposition Cambodia National Rescue Party. The CNRP says it was cheated out of a victory and will boycott the new Parliament until the government has met its demands.
The new demonstrations coincide with the 22nd anniversary of the 1991 Paris Peace Agreements on Cambodia, which laid the groundwork for U.N.-sponsored elections after the brutal rule of the Khmer Rouge and years of civil war that followed. Opposition leaders say that in the next two days they will deliver petitions to several embassies of countries that signed the agreements, including France, Britain and the U.S.
More than 1,000 police and soldiers were put on duty for the protest, which authorities said they would allow as long as there is no violence. Military police spokesman Kheng Tito has said authorities were ordered to take a softer line on this rally than on one in September, when clashes with police left one man dead and several injured.
Opposition leader Sam Rainsy assured the protest would be peaceful. "If there is any violence, it will not come from us," he said.
Human Rights Watch echoed the CNRP's calls for an investigation.
"Cambodia's donors and other countries should publicly press the Cambodian government to set up an independent, internationally assisted investigation into disputed national elections in July 2013," the New York-based rights group said in a statement Wednesday.
The group's Asia director, Brad Adams, criticized France, Australia and Japan for sending congratulatory letters to Prime Minister Hun Sen, saying in the statement that "democratic leaders should skip the congratulations and instead insist on an independent investigation into malfeasance at the polls."
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Associated Press writer Sopheng Cheang contributed to this report.