* Georgian billionaire discusses his future cabinet
* Says United States is main partner
* Cohabitation with president could be awkward
By Margarita Antidze and Steve Gutterman
TBILISI, Oct 3 (Reuters) - Georgia's richest man began talks on forming a government for the former Soviet republic on Wednesday and addressed fears over his links with Moscow by saying his first visit abroad would be to the United States.
Billionaire Bidzina Ivanishvili urged President Mikheil Saakashvili, a staunch U.S. ally, to resign following Monday's parliamentary election, which the president conceded his party had lost to Ivanishvili's coalition.
Saakashvili, who has dominated Georgian politics for almost a decade, has not commented, but allies say he will see out his final term, which ends next year, setting up an awkward period of cohabitation.
Western governments joined many Georgians in welcoming Saakashvili's acceptance that his party had lost an election some had feared would ignite unrest in the Caucasus nation, a conduit of energy supplies to Europe.
Ivanishvili, 56, has made clear he plans to be prime minister, Georgia's most powerful executive official once reforms weakening the head of state take effect after the presidential vote expected some time in 2013.
A political novice who made his fortune mainly in Russia, has acknowledged his six-party coalition is fragile and that he faces a difficult balancing act between the West and Moscow, which welcomed his election victory as a chance for better ties.
Saakashvili avidly sought NATO membership for Georgia and fought a brief war in 2008 with Russia, whose leaders portray him as unbalanced.
Ivanishvili says he wants to mend ties with Moscow and denies Saakashvili's accusations he is a Russian stooge.
"My first visit abroad will be to Washington and the United States is our main partner," Ivanishvili told reporters on Wednesday.
He met leaders from his Georgian Dream coalition to discuss portfolios in a government to be formed by Oct 20 which he has said would include no current ministers. He has acknowledged that it could break up into three factions in parliament.
Saakashvili, who has the power to veto both a cabinet line-up and future legislation, said he would not hinder Georgian Dream's efforts to form a government but that some of its views were "fundamentally unacceptable". He did not elaborate.
The president, who swept to power after the bloodless 2003 Rose Revolution street protests over alleged election fraud, has been accused of authoritarianism by his rivals.
His acceptance that his ruling United National Movement party will go into opposition strengthened Georgia's democratic credentials and increased the chances of its first peaceful transfer of power between rival parties since the Soviet Union collapsed in 1991.
"They had enough common sense to end all this peacefully and Mikheil Saakashvili conceded defeat and said he would become the opposition now," said Merab, a Tbilisi resident who declined to give his last name. "This is very good, I only welcome this."
But nearly complete election results show Saakashvili's United National Movement will be a large minority, and with Ivanishvili's call on Tuesday for Saakashvili's resignation, the potential for confrontation remains.
"It is still possible that there will be disturbances or street protests if the two sides cannot agree on what is going to occur in the next year," said Lawrence Sheets, South Caucasus project director for the International Crisis Group.
He also said there could be "witch hunts" against allies of Saakashvili, who opponents accuse of trampling human rights and suppressing dissent.
Ivanishvili said there would be "no persecution" of supporters of Saakashvili as long as they did not break the law.
"We will have a working relationship with the president," Irakli Alasania, a senior Georgian Dream member, told reporters.
While vibrant celebrations by supporters waving blue Georgian Dream flags following the election underscored the high hopes many Georgians have in Ivanishvili, he is an unknown quantity and some wonder about his ability to govern.
Russia welcomed the election result and said on Wednesday that it hoped diplomatic relations - severed over the war - could eventually be restored.
"It is obvious that Georgian society has voted for changes. We hope in the end they will allow Georgia to start the normalisation, establishment of constructive and respectful relations with neighbours," Russian Foreign Ministry spokesman Alexander Lukashevich said in the statement.
"Such a development would be welcomed in Russia," he added.
Fyodor Lukyanov, a Russian foreign policy analyst, told Reuters Moscow realised the Georgian public supported ties with the West and NATO and that any leader needed to reflect that to preserve public support.
"Russia understands it well and will try to ignore it," he said. "Russia is keen to demonstrate that when 'normal' people are in power in Georgia, it can deal with them perfectly fine."
Ivanishvili faces an uphill struggle to improve the economy which contracted in 2009, hit by the 2008 war and the global economic crisis. It has started growing again but the official unemployment rate of 16 percent is considered an underestimate.
He has pledged to fight corruption and poverty, and to reduce bureaucratic controls, end monopolies and take steps to woo foreign investors. He says he will improve health care and agriculture, make the justice system more independent and ensure the tax and customs departments are more transparent.
Tbilisi resident Georgy Ubiria said the country would benefit from having two influential parties.
"I think that there should be two major forces in Georgia, not just one force that is ruling the country. There will be more control, and this will be very good for Georgia," he said.