Moscow (CNN) -- Russian Prime Minister Vladimir Putin called for unity as he appeared headed for a third term as president, declaring victory in an "open and honest fight" in Sunday's election.

But chess champion-turned-opposition activist Garry Kasparov accused Putin's supporters of "massive fraud" early Monday by packing the polls with additional voters.

With better than two-thirds of the vote reporting early Monday, Putin led his closest rival by a nearly 4-to-1 margin. His margin of victory was smaller than in 2004, the last time he ran for president, but appears well above the 50% needed to avoid a runoff.

"We have won an open and honest fight," Putin told the cheering and flag-waving supporters who had braved the cold in Manezhnaya Square for hours to hear his expected victory speech. The results show "that our people are ready for renewal, and have only one aim."

"We are appealing to all people to unite for our people, for our motherland, and we will win," he said. "We've had a victory! Glory to Russia!"

The 59-year-old former KGB officer served two terms in the Kremlin before term limits forced him to step down in 2008. But he served as prime minister under his successor, Dmitry Medvedev, and continued to dominate Russian politics.

With more than 68% of boxes reporting, Putin had just under 65% of the vote in a field of five candidates. His closest challenger, Communist leader Gennady Zyuganov, had slightly more than had 17%; the other three candidates -- including billionaire Mikhail Prokhorov, the owner of the New Jersey Nets basketball team -- were running in the single digits.

Critics have long accused Putin of undermining Russia's democratic institutions during his years in power, and accusations of voter fraud in December's parliamentary elections have led to unprecedented public protests against his government. But Ivan Zassoursky, a media analyst at Moscow State University, told CNN the demonstrations may have helped Putin consolidate his support.

"He was able to mobilize his core electorate -- the workers, the blue-collar workers, the state workers -- all the people that the state pays salaries to, all the people that the state gives order to, like industrial complexes," Zassoursky said.

"I think they all have been shaken and stirred by the fact that the opposition has so many people, that they are so vocal, and I think this has pulled them into action."

But opposition figures said they planned to continue their demonstrations as early as Monday, fueled by new complaints about Sunday's results.

Kasparov, who served as a poll watcher in his Moscow neighborhood, said Putin's supporters "simply added new voters to the register using so-called supplementary voter rolls."

"At one of the polling stations, the number of extra voters even exceeded the number of registered voters," he said.

And Ilya Ponomarev, a member of parliament and a prominent protest figure, said he did not feel there was a fair counting of votes. Many polls before the vote, he said, showed Putin receiving around 40%.

"Mr. Putin remains to be one of the most popular politicians in the country, probably the most popular politician in the country, and it's quite natural that he's receiving the majority of the votes," Ponomarev, of the A Just Russia party, told CNN from Moscow's Red Square. "But it should not be an overwhelming majority, and I think there has to be a runoff."

But in the run-up to Sunday's voting, Putin's spokesman played down the public protests over the past three months.

"It's pure mathematics," Dimitri Peskov said. "Yes, we have something like 70,000 people out there (protesting) on Sakharov Avenue, but at the same time we have to keep in mind they are a minority. The majority of the population does not live here in Moscow. We have a huge country and if we look eastwards, we'll see lots and lots of big cities, small towns and rural populations that still support Putin pretty well."

Three policemen were killed in an attack on a polling station in Russia's southern republic of Dagestan after voting closed Sunday, police spokesman Alexander Gorovoy said. One of the attackers, who all wore masks, was also killed, he said.

Violence has plagued the republic for years, with Islamist rebels fighting Moscow rule in the region, and Gorovoy said the Interior Ministry would vigorously investigate the attack.

Of Putin's opponents, Prokhorov -- Russia's third-richest man -- was the only fresh face in the pack. Zyuganov is a serial election loser now facing his fourth defeat, while right-wing candidate Vladimir Zhirinovsky and left-leaning Sergey Mironov also have run and lost previous campaigns.

On paper, Prokhorov 's manifesto of democratic and economic reforms should have appealed to many of Moscow's voters, but he struggled to shake a reputation of being too close to the regime. Cynics call him a Kremlin project, a candidate designed to credibly attract the middle-class vote without posing a genuine threat.

CNN's Jill Dougherty contributed to this report.