MOSCOW (AP) — Prime Minister Vladimir Putin on Sunday claimed victory in Russia's presidential election before tens of thousands of cheering supporters, even as the opposition and independent observers insisted the vote had been marred by widespread violations.

At a massive rally just outside the Kremlin, Putin thanked his supporters for helping foil plots aimed at destroying Russia, sounding a nationalistic theme that has resonated with his core supporters.

"I have promised that we would win and we have won!" he shouted to the flag-waving crowd, which responded with shouts of support. "We have won in an open and honest struggle."

Putin tallied 58-59 percent of Sunday's vote, according to exit polls cited by state television. Communist Party candidate Gennady Zyuganov received about 18 percent, according to the survey, and the others — nationalist Vladimir Zhirinovsky, socialist Sergei Mironov and billionaire Mikhail Prokhorov — were in single digits.

Official vote results from the far eastern regions where the count was already completed seemed to confirm the poll data. With about 30 percent of all precincts counted, Putin was leading the field with 64 percent of the vote, the Central Election Commission said.

If thousands of claims of violations made by independent observers and Putin's foes are confirmed, they would undermine the legitimacy of his victory and fuel protests. The opposition is gearing up for a massive rally in downtown Moscow on Monday.

"These elections are not free ... that's why we'll have protests tomorrow. We will not recognize the president as legitimate," said Mikhail Kasyanov, who was Putin's first prime minister before going into opposition.

Golos, Russia's leading independent elections watchdog, said it received numerous reports of "carousel voting," in which busloads of voters are driven around to cast ballots multiple times.

Alexei Navalny, one of the opposition's most charismatic leaders, said observers trained by his organization also reported seeing extensive use of the practice.

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Evidence of widespread vote fraud in December's parliamentary election drew tens of thousands to protest against Putin, who was president in 2000-2008 before moving into the prime minister's office due to term limits. They were the largest outburst of public anger in post-Soviet Russia and demonstrated growing exasperation with massive corruption, rising social inequality and tight controls over political life under Putin.

Putin has dismissed the protesters' demands, casting them as a coddled minority of urban elites working at Western behest to weaken Russia. His claims that the United States was behind the opposition protests spoke to his base of blue-collar workers, farmers and state employees, who are suspicious of Western intentions after years of state propaganda.

"Putin is a brave and persistent man who can resist the U.S. and EU pressure," said Anastasia Lushnikova, a 20-year old student who voted for Putin in the southern city of Rostov-on-Don.

Authorities gave permission to Putin's supporters to gather just outside the Kremlin walls, and tens of thousands flooded the big square immediately after the vote ended. Some participants of the demonstration, including employees of state organizations, said they were forced by the management to attend it under the threat of punishment.

The authorities denied the opposition's bid to hold the rally at the same place Monday, but allowed them to gather at a nearby square.

Putin has given generous social promises during his campaign and also initiated limited political reforms in a bid to assuage public anger. His spokesman Dmitry Peskov said Sunday that Putin will seek to modernize the nation's political and economic system, but firmly ruled out any "Gorbachev-style liberal spasms."

Mikhail Gorbachev, the last leader of the Soviet Union, has become increasingly critical of Putin's rule. "These are not going to be honest elections, but we must not relent," he said Sunday after casting his ballot.

Putin has promised that the vote would be fair, and the authorities apparently have sought to take off the steam out of the protest movement by allowing more observers to monitor the vote. Tens of thousands of Russians, most of them politically active for the first time, had volunteered to be election observers, receiving training on how to recognize vote-rigging and record and report violations.

Golos said monitors have recorded fewer obvious violations than during the December election, but they still believe that violations are extensive. This time, election officials are using more complicated and subtle methods, said Golos deputy director Grigory Melkonyants.

According to data based on official figures from polling stations attended by Golos observers, Putin still garnered some 55 percent of the vote, while Zyuganov won about 19 percent.

Zyuganov told reporters after the polls closed that he will not recognize the vote, calling it "illegitimate, unfair and intransparent."

His campaign chief Ivan Melnikov claimed that the authorities set up numerous additional polling stations and alleged that hundreds of thousands of voters cast ballots at the ones in Moscow alone in an apparent attempt to rig the vote.

Prokhorov said on Channel One television after the vote that authorities kept his observers away from some polling stations and were beaten on two occasions.

Oksana Dmitriyeva, a Duma deputy from Just Russia party, tweeted that they were witnessing "numerous cases of observers being expelled from polling stations" across St. Petersburg just before the vote count.

Unlike Moscow and other big cities, where independent observers showed up en masse, election officials in Russia's North Caucasus and other regions were largely left to their one devices. The opposition said those regions have experienced particularly massive vote rigging in the past.

A Web camera at a polling station in Dagestan, a Caucasus province near Chechnya, registered unidentified people tossing ballot after ballot into boxes. The Central Election Commission quickly responded to the video, which was posted on the Internet, saying the results from the station will be invalidated.

Web cameras were installed in Russia's more than 90,000 polling stations, a move initiated by Putin in response to complaints of ballot stuffing and fraudulent counts in December's parliamentary elections.

It was unclear Sunday to what extent the cameras would be effective in recording voting irregularities or questionable counts. The election observation mission of the Organization for Security and Cooperation in Europe noted skepticism in a report on election preparations.

"This is not an election ... it is an imitation," said Boris Nemtsov, a prominent opposition leader.

But despite the increased resentment against Putin's rule among the rising middle class, opinion polls ahead of the vote had shown Putin positioned to win easily. He presided over significant economic growth and gave Russians a sense of stability that contrasted with the disorder and anxiety of the 1990s, when Boris Yeltsin led Russia's emergence from the wreckage of the Soviet Union.

"Under Boris Nikolayevich, life was simply a nightmare, but, you know, now it's OK. Now it's good, I'm happy with the current situation," said 51-year-old Alexander Pshennikov, who cast his ballot for Putin at a Moscow polling station.

The police presence was heavy throughout the city on Sunday. There were no immediate reports of trouble, although police arrested three young women who stripped to the waist at the polling station where Putin cast his ballot; one of them had the word "thief" written on her bare back.

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Jim Heintz, Lynn Berry, Maria Danilova, Nataliya Vasilyeva, Mansur Mirovalev and Sofia Javed in Moscow and Sergei Venyavsky in Rostov-on-Don contributed to this report.