The president says she won't step down on Monday, when the newly elected president, Mikheil Kavelashvili, is due to take over.
ADVERTISEMENTGeorgia's current president joined thousands of protests in the streets of the capital Tbilisi on Saturday, exactly a month after opposition protests broke out.
Zourabichvili has said she will defy the results of the legislative elections in October and remain in office after Monday.
And she's been calling for a new vote, claiming that the elections were manipulated by Russian interference.
The Organisation for Security and Cooperation in Europe (OSCE), which monitored the election, also called the election into question.
“Numerous issues noted in our final report negatively impacted the integrity of these elections and eroded public trust in the process,” Eoghan Murphy, who headed its election observation mission, said on 20 December.
In Tbilisi the protesters attempted to form a human chain snaking over all of the capital's eight bridges across the Kura river.
There were also protests in other cities on Saturday against Prime Minister Irakli Kobakhidze.
His ruling Russian-friendly Georgian Dream party was founded by the shadowy billionaire Bidzina Ivanishvili. On Friday the United States slapped fresh sanctions on him, saying he was undermining democracy to the benefit of Russia.
The protests began on 28 November after Kobakhidze announced that Georgia would postpone its EU bid until 2028. Since then, there has been a steady flow of people rallying during the day and remaining out through the night.