The hotly contested race pits ex-French ambassador and Georgia's former foreign minister Salome Zurabishvili, supported by the ruling Georgian Dream party, against opposition leader Grigol Vashadze, also a former foreign minister.
The first officials results from Georgia's presidential election on Sunday showed that neither of the two frontrunners was likely to win enough votes to secure victory and they would face a second round run-off vote.
The head of the Central Election Commission, Tamar Zhvania, said that according to results from 13 percent of the polling stations, Salome Zurabishvili had secured 40.05 percent of the vote and Grigol Vashadze had won 37.93 percent.
The ruling Georgian Dream Party, whose candidate is French-born former foreign minister Zurabishvili, said that she would meet opposition candidate Vashadze in an election run-off.
Zurabishvili's supporters say she would bring international stature to the presidency; opponents criticise her for statements that appeared to blame Georgia for war with Russia in 2008, remarks about minorities that some saw as xenophobic, and unsteady command of the Georgian language, which she speaks with an accent.
Vashadze is running on behalf of a new platform of 11 opposition parties led by former president Mikheil Saakashvili's United National Movement (UNM). He held the post of foreign minister from 2008-2012.
Constitutional changes have weakened the power of Georgia's presidency, putting most authority in the office of prime minister.
But the post is still seen as important for the image abroad of a country strongly oriented towards the West and fearful of Russia, which invaded a decade ago and backs separatists in two breakaway regions.
Sunday's election will also be the last in which the president is selected by popular vote; after that, presidents will be picked by an electoral college of 300 lawmakers and regional officials.
Who is Zurabishvili?
Zurabishvili was invited into Georgian politics by Saakishvili, who gave her Georgian citizenship to take up the foreign ministry post but sacked her after a year.
She then set up her own opposition political party, Georgia's Way, which she led until 2010 before temporarily quitting politics and returning to France.
She was elected to Georgia's parliament in 2016 with the backing of Georgian Dream, a party controlled by Bidzina Ivanishvili, the country's richest man, whose critics say he rules it from behind the scenes.
The two frontrunners are followed by David Bakradze, a former parliamentary speaker, who has been nominated by the opposition European GeorgiaParty, which split from the UNM in 2017.
The country of 3.7 million people is Washington's strategic ally in the Caucasus region between the Black Sea and Caspian Sea, and hopes eventually to join the EU and NATO.
Pipelines carrying Caspian oil and gas to Europe run across its territory.