* First results show Georgian Dream ahead in party-list voting
* Opposition tycoon confident of big majority in parliament
* Ruling party issues rival claim as opposition celebrates
* Prison abuse scandal video undermines Saakashvili
By Margarita Antidze and Steve Gutterman
TBILISI, Oct 2 (Reuters) - An opposition coalition led by a billionaire tycoon claimed victory in a parliamentary election in Georgia and initial results released on Tuesday put it ahead of President Mikheil Saakashvili's ruling party in the former Soviet republic.
Thousands of supporters of the Georgian Dream coalition celebrated in the streets of the capital Tbilisi after the election on Monday, sounding car horns and carrying blue party banners and red-on-white national flags over their heads.
"I expect that we will get no less than 100 seats in the new (150 seat) parliament," the coalition's leader, wealthy tycoon Bidzina Ivanishvili, told a cheering crowd. "I have achieved what I have long been striving for."
But a tense stand-off loomed over the results of the poll, which under Georgia's electoral system allocates 77 of the 150 parliament seats according to party lists and the other 73 according to constituent victories.
With ballots from six percent polling stations counted under the party list system, Georgian Dream had 56.1 percent and Saakashvili's United National Movement had 39.4 percent, the Central Election Commission said on its website.
But the UNM said it believed it had won at least 53 of the 73 seats allotted in elections tallied according to individual constituencies, results of which had not yet been released.
"This means that the United National Movement will have a majority in the new parliament," spokeswoman Chiora Taktakishvili said in televised comments on Monday.
Any signs of instability in the Caucasus country of 4.5 million would worry the West because of its role as a conduit for Caspian Sea energy supplies to Europe and its strategic location between Russia, Iran, Turkey and central Asia.
Saakashvili says the Georgian Dream coalition would move Georgia away from the West and back into Moscow's orbit, and has suggested Ivanishvili is doing the bidding of the Kremlin after making his money in Russia.
Ivanishvili, a former reclusive who entered politics only a year ago, told Reuters he was confident Georgian Dream candidates had won at least 50 of the individual races.
"A very interesting precedent has been set in which the leadership has been replaced through elections," he said after exit polls predicted Georgian Dream beat out the ruling party in the party-list voting.
GEORGIAN DREAM SUPPORTERS CELEBRATE
Georgian Dream's strong showing was an indictment of Saakashvili, who swept to the presidency in the bloodless Rose Revolution of 2003 but led Georgia into a disastrous five-day war with Russia over two breakaway regions in 2008.
Saakashvili cautioned that the results were not yet in, and the U.S. ambassador earlier on Monday urged Georgians to "stay calm" until votes were counted and any challenges addressed.
Saakashvili must step down after a presidential election next year, when reforms weakening the head of state and giving more power to parliament and the prime minister are to take effect.
If his party retains control of parliament, it may give him a way to keep calling the shots. If not, Ivanishvili could become premier and Georgia's dominant politician.
"Besides being a contest for parliament, it is also a shadow leadership election," said Thomas de Waal, a Caucasus expert at the Carnegie Endowment for International Peace in Washington.
In a televised address after polls closed, Saakashvili, 44, said it appeared Georgian Dream had prevailed in the party-list voting but his party had come out ahead in the individual races.
When parliament convenes, ruling party and opposition deputies should "take their seats and start working in a joint democratic process", he said. "We are all Georgian citizens, we should stand together and work together."
But the exit polls emboldened Georgian Dream supporters and could lead to increased tensions if their strong showing is not matched by results in the individual districts - an outcome that could stoke suspicions of rigging.
Tension was already high after video footage of torture, beatings and sexual assault of prison inmates led to street protests after it was aired on two television channels opposed to Saakashvili about two weeks before the election.
The footage undermined Saakashvili's image as a reformer who had imposed the rule of law and rooted out corruption.
"I'm voting against violence and abuse. How can I do otherwise after what we have all seen on TV?" Natela Zhorzholiani, 68, said as she voted in Tbilisi.
Ivanishvili has won votes by promising to tackle poverty and corruption, blaming these problems on Saakashvili, although not everyone trusts him to do better than the current president and Saakashvili portrays him as open to Russian manipulation.
"I voted for peace and stability," Georgy Ugrekhelidze, 76. "I want this government to carry out what it has started."
Opponents accuse Saakashvili of monopolising power, curtailing democracy and suppressing dissent. He owes his rise to power to street protests over claims of election fraud, but has damaged his image by cracking down on opponents.
Police used teargas, rubber bullets and water cannons to disperse protesters in Tbilisi in November 2007. Security forces again cracked down on protesters in 2010 after opponents occupied a central square.
Georgia's Central Election Commission said there were no grave violations during the voting on Monday, but a confrontation did erupt in the central town of Khashuri late Monday night after ballots were counted.
Citing an observer, Transparency International Georgia said armed men forced their way into two polling places in Khashuri and, in one of them, a protocol that had shown Georgian Dream winning more votes was replaced by one making UNM the winner.
Opposition television channels showed footage of shouting crowds and riot police they said fired teargas and rubber bullets. The Interior Ministry said police were sent to guard polling stations and denied the use of teargas or guns.