The governing party was in a heated race against an opposition coalition led by Bidzina Ivanishvili, a billionaire businessman who has posed the most serious challenge to the pro-Western president since he came to power almost nine years ago.
No results have been released yet in Monday's vote. Two exit polls conducted by Edison Research and Gfk gave the edge to the opposition, but they were done four hours before the voting stations closed and registered only the vote based on party lists, which is used to elect 77 of parliament's 150 members.
The remaining 73 members are directly elected by majority vote in their constituencies, where the president's United National Movement is considered to have a strong advantage.
Saakashvili, speaking on television shortly after the polls closed, said the opposition coalition Georgian Dream had indeed won the party vote, largely on the strength of its support in the capital, Tbilisi. Still, he said his party was far ahead in the direct elections and would retain its majority in parliament.
Georgian Dream, however, released a statement saying that its own exit polls showed it would win the party vote by 63 percent and cited Ivanishvili saying he was "prepared to ensure a parliamentary majority."
The Central Election Commission said the first preliminary results were expected at 3 a.m. Tuesday (2300GMT, 7 p.m. EST Monday).
Emotions were running high, but both sides have promised to respect the results if the election receives the approval of international observers.
The U.S. ambassador joined calls for a peaceful election.
"I encourage the public to remain calm, have faith and be patient while all the results are counted and any challenges are properly evaluated," Ambassador Richard Norland said.
Under Saakashvili, the former Soviet republic has aligned itself with the United States, while striving to join the European Union and NATO.
Ivanishvili, who made his money in Russia, has said he would pursue these strategic goals while also seeking to restore the ties with Moscow that were severed when the two neighboring countries fought a brief war in 2008.
Saakashvili has accused Ivanishvili of serving Kremlin interests and intending to put Georgia back under Russian domination, which the opposition leader has denied.
After casting his vote on Monday, Saakashvili said the election was important not only for Georgia, a nation of 4.5 million on the Black Sea, but for the region.
"A lot of things are being decided right now in our country ... for the future not only of this nation, but for what happens to the European dream in this part of the world, what happens to the idea of democracy in this part of the world, what happens to the idea of reforms in this part of the world." he said, his Dutch wife and their young son standing behind him.
The opposition has accused 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."
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 Saakashvili had 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 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."
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.
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."
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.
Saakashvili won a presidential election in January 2004 with 96 percent of the vote and reelection 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 Saakashvili's second and last term ends next year, many of the president's powers will be transferred to the prime minister.
If 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.
Ivanishvili is not running for a seat in parliament, but has said that if his Georgian Dream coalition wins he would serve as prime minister at least for a year or two to put his team in place.
(Copyright 2012 by The Associated Press. All Rights Reserved.)