Georgia on Sunday inaugurated its new president, Giorgi Margvelashvili, replacing charismatic reformer Mikheil Saakashvili after a decade at the helm of the ex-Soviet country.

Margvelashvili, a close ally of Saakashvili's arch-foe, billionaire Prime Minister Bidzina Ivanishvili, cruised to victory with around 62 percent of the vote at an election last month.

A French court on Thursday rejected a detained former Georgian defense minister's plea to be set free but did not rule on his extradition to his homeland, where he is wanted on corruption charges.

Davit Kezerashvili, a close ally of outgoing president Mikheil Saakashvili, was detained on October 14 at Nice airport following an international arrest warrant.

European Commission head Jose Manuel Barroso called Tuesday on Georgia's new president to build on the political and economic gains of his predecessor, by respecting the rule of law and democracy.

Speaking with outgoing President Mikheil Saakashvili, Barroso said "it is important that we share the same values as we bring Georgia closer to Europe ... Georgia must remain a pluralistic democracy."

Georgian president-elect Giorgi Margvelashvili on Monday said he would strive to reduce tensions with Russia after the two foes fought a brief 2008 war under outgoing leader Mikheil Saakashvili.

"The relations are extremely difficult," Margvelashvili told reporters after sealing a landslide win at elections on Sunday.

An ally of billionaire Georgian Prime Minister Bidzina Ivanishvili claimed a crushing first-round victory in a presidential vote Sunday after his main opponent conceded defeat and exit polls pointed to an overwhelming win.

Giorgi Margvelashvili, a little-known academic from the premier's Georgian Dream coalition, had at least 66 percent of the vote in two television exit polls, well ahead of former parliament speaker David Bakradze of outgoing President Mikheil Saakashvili's United National Movement party, in second place with around 20 percent in the ex-Soviet state.

French authorities have detained a former Georgian defense minister wanted in his homeland on corruption charges, Georgia's interior ministry said Tuesday.

Davit Kezerashvili, a close ally of outgoing president Mikheil Saakashvili, was detained Monday in Paris and is set to face an extradition hearing to determine whether he should be sent back to the Caucasus nation.

Some 12,000 supporters of outgoing President Mikheil Saakashvili's United National Movement (UNM) party rallied in the Georgian capital Tbilisi on Saturday in a show of strength ahead of presidential polls.

Saakashvili, who has to step down when his second and last term ends at the October 27 election, has been seen as a lame duck ever since his party lost to the Georgian Dream coalition headed by billionaire Prime Minister Bidzina Ivanishvili at parliamentary polls last year.

Georgia on Wednesday voiced "extreme concern" over the presence of Russian troops in its breakaway regions of Abkhazia and South Ossetia.

"I must express our extreme concern over the critical situation in the two regions of Georgia currently under the Russian occupation," Foreign Minister Maia Panjikidze told the U.N. Human Rights Council in Geneva.

A two-metre high statue of Soviet leader Joseph Stalin has been daubed with paint less than a day after it was put up in a town in eastern Georgia, local authorities said Monday.

Local authorities in the town of Telavi, some 100 kilometres east of Tbilisi, said the monument to the Georgian-born Communist dictator was erected without permission by local residents on Sunday and could be torn down.

Georgia on Thursday marked the fifth anniversary of the 2008 war with Russia over Georgia's separatist territory of South Ossetia, with both sides still blaming each other for the costly conflict.

The government is holding a series of sombre events to commemorate the occasion, including a wreath-laying ceremony in Tbilisi at a cemetery for servicemen killed in the fighting and a military parade in the town of Gori -- which was bombed and briefly occupied by Russian forces.