In exit polling, the private Imedi TV channel said Georgian Dream would win about 50 percent of the vote. A separate exit poll reported by the Georgian Public Broadcaster had Georgian Dream and ENM level at 33 percent. Under Georgia's complicated mixed member majoritarian system, it is as yet unclear how the seats in parliament will be allocated.
The Central Election Commission said with ballots from 10 percent of polling stations counted under the party list system, Georgian Dream had 57 percent and ENM had 38 percent.
Saakashvili, speaking in televised remarks after the polls closed, acknowledged that Georgian Dream had won the party vote. But he said his ENM -- which currently holds nearly 80 percent of the seats in parliament -- was far ahead in the direct elections and would retain its parliamentary majority.
Ivanishvili told cheering supporters in the capital, Tbilisi, that he believed Georgian Dream would dominate the assembly.
"I expect that we will get no less than 100 seats in the new parliament," he said. "I have achieved what I have long been striving for."
Georgia's Central Election Commission said preliminary results will be released early on October 2.
Ahead of the voting, most observers saw the race as too close to call.
The election is seen as crucial because -- with Saakashvili's second and final term to end next year -- the country's political system is being altered to give more power to parliament and prime minister.
Saakashvili cast his ballot at a polling station in Tbilisi early on election day, saying that "the fate of the Georgian state is being decided."
"Lots of things are being decided right now in our country for the region, for development, for the future not only of this nation but of 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."
PHOTO GALLERY: Jubilant Georgian opposition supporters
Saakashvili rose to power in 2004 after the Rose Revolution that toppled Eduard Shevardnadze, a former Soviet foreign minister.
But critics have accused Saakashvili of subsequently monopolizing power and criticized him for leading Georgia -- a country of 4.4 million -- into a disastrous five-day war with Russia in 2008.
In a speech on Georgian television on the eve of voting, Saakashvili urged voters to cast their ballots "based on reason and not on emotions." He called election day "a very important and crucial question is to be decided: which country we want to have. And even more, if we want to have our own country at all."
At a mass rally in Tbilisi on September 29, Ivanishvili -- who made his fortune in Russia -- countered the president’s contention that he will take Georgia back under Russian domination.
"We are the team which you can trust," Ivanishvili said. "We are the team that will take the power into our hands and use it for the benefit of the people. We should win in elections."
On Their Guards
Opposition leaders urged voters to go to the polls, saying a high turnout would help “prevent possible falsifications.”
Catholicos-Patriarch of Georgia Ilia II expressed hope that the elections would “proceed peacefully, and its result will not be falsified."
OSCE observers have described the election campaign as "confrontational and rough."
"We have said publicly, as the parliamentary assemblies gather here to observe these elections, that we want this to be a calm process, that we want the election to be decided in the ballot boxes, not on the streets," OSCE Parliamentary Assembly spokesman Neil Simon said ahead of the voting.
PHOTO GALLERY: Georgians go to the polls
The last time Georgia held parliamentary elections, in 2008, OSCE observers said the poll was marred by a number of flaws.
The run-up to the October 1 vote has seen mass protests against police brutality in prisons after a video emerged of prison abuse.
Fourteen political parties and two blocs are standing for the 150-seat parliament, which is elected for a four-year term.
Seventy-seven seats will go to politicians elected on party tickets, and the remaining 73 will be selected in individual races.
In the party-list voting, a party needs to win at least 5 percent of the vote to gain representation in parliament, and a bloc needs to win at least 7 percent.
Maja Kocijancic, a spokeswoman for EU foreign policy chief Catherine Ashton, said in Brussels as voting took place that the way the election is carried out is importation for relations between the European Union and Tbilisi.
"We have made it very clear that the expectations of these elections are extremely high and that they will determine the pace and the intensity of our relations with Georgia," Kocijancic said.
Under Georgia’s election code, elections are recognized valid regardless of the turnout.