The pro-Western opposition has refused to recognise the ruling Georgian Dream party's win in the October 26 election or to enter the newly elected parliament, which it calls "illegitimate".
The European Union and the United States blasted "irregularities" in the vote, while Georgian Dream's opponents have accused it of putting the Caucasus country on a pro-Kremlin track.
Protesters gathered outside Georgia's parliament on Monday evening, blocking traffic on Tbilisi's main road, after opposition groups called on supporters to take to the streets.
"The Georgian people will never accept falsified election results, an invincible protest movement is rising up and it will sweep away the regime, which has stolen our votes," the leader of the Akhali party, Nika Melia, told the crowd.
He vowed daily protests, with the next rally set for Tuesday.
Mamuka Khazaradze, leader of the Coalition for Change, said: "We demand a fresh vote, an international investigation into election falsification, and we will not surrender until our objectives are met."
President Salome Zurabishvili -- who is at loggerheads with the governing party -- also called the vote "illegitimate" and accused Russia of interference.
Moscow has denied meddling.
"We have no choice but to take to the streets every day to show our government and the world that Georgians will never put up with rigged elections," one of the demonstrators, 25-year-old shop assistant Lidia Kirtadze, told AFP.
Protesters have accused Georgian Dream of derailing the country's goal of joining the European Union.
"Russia and its stooges in our government want to steal not only the choice of the Georgian people but also our European future," said Leo Grigalashvili, a 49-year-old winemaker.
"We will never accept this."
'We need concrete actions'
Ahead of the election, Brussels had warned it would determine Georgia's chances of joining the bloc.
"The situation following the elections remains concerning," EU chief Ursula von der Leyen told Zurabishvili during a phone call on Monday.
"If Georgia wants to keep a strategic orientation towards the EU, we need concrete actions from the leadership," she said on X.
On Monday, a court in Georgia's southern town of Tetritskaro ordered the annulment of election results from several precincts over violations of ballot secrecy.
Georgian rights groups said the ruling sets an important judicial precedent as the same violation had been observed at around 70 percent of polling stations.
A group of Georgia's leading election monitors said earlier that they had uncovered evidence of a complex scheme of large-scale electoral fraud that swayed results in favour of Georgian Dream.
Prosecutors have opened an investigation into the alleged fraud.
Monday's protest came after tens of thousands gathered in a demonstration in the capital city last week.
Prime Minister Irakli Kobakhidze has said the elections were "entirely fair."
But critics have blamed his increasingly conservative Georgian Dream for bringing Tbilisi back into Moscow's orbit.
