The Central Election Commission said the ruling Georgian Dream party won 48.23% of the vote, with the largest opposition party United National Movement (UNM) taking 27.18%.
After the result gave the ruling party the right to form a government, eight opposition parties, including the UNM, said they would boycott the parliament.
The opposition accuses the ruling party and its supporters of vote buying, making threats against voters and local observers and of violations during the counting process. Georgian Dream leaders have denied the accusations.
"This regime and this government are illegitimate... these results are illegitimate," Nika Melia, a UNM leader, told thousands of protesters, most of them wearing protective masks due to the coronavirus concerns.
An alliance of more than 30 opposition parties gave Bidzina Ivanishvili, the founder of Georgian Dream and the country's wealthiest man, a Sunday night deadline to dismiss Tamar Zhvania, head of the electoral commission, and to start talks on a fresh vote.
There has so far been no response from Ivanishvili or the government.
Critics say billionaire Ivanishvili, who does not hold a government post, runs the country of 3.7 million people from behind the scenes, an accusation denied by Georgian Dream, which has governed for two consecutive terms.
The country's economy has been hit hard by the coronavirus outbreak. The government said on Saturday the South Caucasus country would impose an overnight curfew from Monday between 10 p.m. and 5 a.m. in its largest cities due to a sharp rise in cases since early September.