Riot police have been deployed around the country's parliament, the focal point of three nights of protests.
Officers again used tear gas and water cannon against protesters into the early hours of Sunday, as they tried to push people away from the parliament building.
Demonstrations were also taking place in the cities of Batumi, Kutaisi, Zugdidi, and other Georgian regions.
"I'm offering this stability for the transition, because what these people on the streets are demanding is a call for new elections in order to restore this country and its European path," said Zourabichvili.
Hundreds of civil servants have signed letters expressing their disapproval of the government's decision to put negotiations with the EU on hold, saying it went against the national interests of Georgia.
Georgian ambassadors to Bulgaria, Netherlands and Italy have also resigned.
The US said on Saturday that it was suspending its strategic partnership with Georgia, citing the government's "various anti-democratic actions".