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The opposition has accused Mr. Saakashvili of authoritarian rule.

“Without a doubt, Saakashvili and all of his people should leave,” said Mamuka Gigienishvili, a 55-year-old physicist who voted in Tbilisi. “We have had enough of him acting like a czar.”

She said his party “labeled anyone with a different opinion a traitor … as if only they were able to lead the country in the right direction.”

Mr. Saakashvili’s campaign was hit hard by the release two weeks ago of shocking videos showing prisoners in a Tbilisi jail being beaten and sodomized. The government moved quickly to stem the anger, replacing Cabinet ministers blamed for the abuse and arresting prison staff, but many saw the videos as illustrating the excesses of his government.

Veriko Berishvili, a 49-year-old small-business owner, pointed to all that Mr. Saakashvili has done to reform Georgia since coming to power in early 2004. She specifically named the disbanding of the corrupt traffic police and creation of a modern force, a widely praised program carried out by Mr. Saakashvili’s longtime interior minister, whom he named prime minister in June.

“I think we should allow this team to fulfill its promises: to improve the situation in agriculture, decide the problem of joblessness, universal health insurance,” she said. “Look at his baby, the police force. It is the best in the former Soviet Union.”

Mr. Saakashvili has taken a zero-tolerance approach to crime, which has eradicated petty corruption and made the streets safe again. The flip side has been a huge increase in the prison population and the power of the prosecutors, who win convictions in more than 90 percent of cases.

He also enacted reforms and attracted foreign investment that together produced dramatic economic growth. Poverty and unemployment rates, however, remain high.

Mr. Ivanishvili, the opposition leader, expressed confidence earlier Monday that his coalition would win.

“For the first time in Georgian history the Georgian people are managing to conduct really democratic elections, or elections which are very close to being democratic because the government has made many violations already,” he said. “There were many violations before election day, and I think there will be violations today, too, but the wisdom of the Georgian people and historic experience has helped us to make it possible for the first time to change the government through elections.”

Mr. Saakashvili came to power after anger over a rigged parliamentary election in November 2003 led to the Rose Revolution and the ouster of Eduard Shevardnadze, who had taken power in 1992 after a military coup.

Mr. Saakashvili won a presidential election in January 2004 with 96 percent of the vote and re-election four years later.

His United National Movement has held 119 of the 150 seats in parliament.

Monday’s election sets in motion a change in the political system that will reduce the powers of the presidency. The party that wins the majority in parliament will have the right to name the prime minister. When Mr.  Saakashvili’s second and last term ends next year, many of the president’s powers will be transferred to the prime minister.

If Mr. Saakashvili’s party wins on Monday, he has said he does not intend to become prime minister after the presidential election in October 2013. Such a job swap would bring unwelcome comparisons to Russian President Vladimir Putin, who served for four years as prime minister to avoid a constitutional ban on more than two consecutive terms as president.

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