Security Council head Vano Merebishvili told state television on Wednesday that the rebel leader had "two or three hours to obey the president".
Some 5000 protesters in the port of Batumi called for Abashidze to step down on Wednesday, their ranks swollen by uniformed policemen and state media workers.
As the groundswell of protest rose, the Georgian government said Ajaria's Black Sea oil port at Batumi had been planted with explosives and the consequences could be catastrophic.
Abashidze's resignation would underpin Georgian president Mikhail Saakashvili's popularity and authority.
Saakashvili, who came to power after a revolution last year, has made reining in Georgia's three rebel regions a priority.
Georgian officials said talks were due on Wednesday evening between the rebel's interior ministry and Georgian Prime Minister Zurab Zhvania.
Rebel leader Aslan Abashidze (R)
came to power with Shevardnadze
Zhvania said Moscow mayor Yuri Luzhkov may mediate. Abashidze has close ties to Moscow - which maintains a military garrison in Ajaria.
But the 65-year old separatist leader said he would never negotiate his resignation and instead has reinforced a state of emergency, closing universities and sending police to disperse demonstrations.
However, Tbilisi has said it would guarantee his safety and give him the chance to leave Ajaria if no blood was spilled.
Georgia is no stranger to civil wars. In the early 1990s, two other regions which refused to answer to Tbilisi, Abkhazia and South Ossetia fought and won separatist wars.
Western governments are watching developments with growing alarm. They are backing a multi-billion-dollar oil pipeline from the Caspian Sea, across Georgia, to a tanker terminal on Turkey's Mediterranean coast.
They fear that instability in Georgia could jeopardise the project.