Early results suggest the opposition Georgian Dream coalition, led by billionaire Bidzina Ivanishvili, had a clear lead in votes for party lists.
But President Mikheil Saakashvili said his ruling party was ahead in the race for seats decided on a first-past-the-post basis – nearly half the total.
It is seen as his biggest popularity test since he came to power in 2003.
The election could bring the first democratic transfer of power in Georgia’s post-Soviet history.
It is not yet clear when official results from Monday’s vote will be announced.
Georgia’s Central Electoral Commission (CEC) said there had been no grave violations during the voting. Observers from the European security organization OSCE are due to give their verdict at 14:30.
According to the CEC’s early results, the rival blocs are running neck-and-neck in the 73 first-past-the-post constituencies.
The other 77 out of 150 parliamentary seats in total are decided by the proportional, party list method.
With 25% of the party list vote counted, Georgian Dream had secured 53%, while Mikheil Saakashvili’s United National Movement (UNM) had 41%.
Mikheil Saakashvili had sought to portray the election as a choice between his Western-leaning government, and a future in which he said Bidzina Ivanishvili would allow Russia to dominate the former Soviet republic. Bidzina Ivanishvili made his fortune in Russia in the early 1990s.
Tensions between Mikheil Saakashvili’s government and Russia escalated into a brief war in 2008 which saw Georgian troops expelled from two breakaway regions.
Thousands of cheering supporters of the opposition Georgian Dream bloc gathered to celebrate in the capital Tbilisi after the polls closed late on Monday.
“We have won! The Georgian people have won!” Bidzina Ivanishvili said in a speech broadcast on a Georgian TV station, the AFP news agency reports.
Bidzina Ivanishvili, Georgia’s richest man, said he expected his coalition to win 100 out of 150 parliamentary seats.
In televised comments, Mikheil Saakashvili conceded the opposition “has won the majority in the proportional vote”.
But he added that “in single-mandate constituencies, the majority of votes has been secured by Georgia’s [ruling] United National Movement”.
The UNM said it believed it had secured at least 53 of the 73 seats in the single-mandate constituencies, with a party’s spokeswoman predicting that it would have “a solid majority”.
The single mandate, first-past-the-post system helps to ensure that rural voters still have a voice. An MP representing a small district in the mountains is equal to one representing a large district in Tbilisi.
Under reforms scheduled to take effect after a presidential election next year the parliament and prime minister will have more power than the president.
The Central Electoral Commission said in a statement that turnout had been around 61%.
Earlier Bidzina Ivanishvili had staged a symbolic protest by refusing to vote, saying the authorities had “already resorted to very many violations”.
If the ruling party gets back into power despite failing to secure a majority of votes, the opposition could feel cheated of victory – and spark mass protests.
The government’s reputation has taken a battering in recent weeks because of a prisoner-abuse scandal.
Videos broadcast on national television showed prison inmates being beaten and sexually abused by guards.
The scandal sparked street protests and allowed Bidzina Ivanishvili to portray the government as high-handed.
Human rights group Amnesty International says many of Bidzina Ivanishvili’s supporters were “fined, fired, harassed or detained for expressing their political views” during the election campaign.
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