President Mikhail Saakashvili gave Adjara's leader Aslan Abashidze until the evening to recognise Tbilisi's authority.
"I am giving Abashidze until tomorrow night for reflection," Saakashvili told reporters at the Ankor Hotel in the coastal town of Poti.
The 36-year-old Georgian leader said he would convene a cabinet meeting at which he will propose closing Adjara's borders and freezing the financing of Adjara's leaders.
"No major cargo will enter or leave tomorrow from the territory of Adjara," he said.
Abashidze arrived in Adjara's capital Batumi early on Monday from Moscow, where he had been lobbying for Russia's support in his standoff with the Georgian leadership.
Russia - which has a military base inside Adjara - has warned the Georgian authorities of "grave and unpredictable consequences" if Georgia sends its forces into the region.
"We will make every effort to resolve this peacefully and calmly. But we will not be forgiving if these people pass the point of no-return... We cannot allow Georgia to break up into pieces"
The crisis flared early on Sunday after armed men loyal to Abashidze blocked Saakashvili and his entourage from driving into Adjara, and fired automatic rounds into the air over his motorcade.
Saakashvili turned around and drove to the nearby city of Poti, where he convened an emergency cabinet meeting, ordered the military onto high alert, and ordered Adjara's airspace shut down.
In Adjara, where authorities declared a curfew early on Monday, there were reports of tanks being mobilised and weapons being handed out to civilians, as Abashidze warned that Saakashvili was planning an armed invasion.
"We will make every effort to resolve this peacefully and calmly," said Saakashvili, who came to power on a promise to bring Georgia's wayward provinces back into line.
"But we will not be forgiving if these people pass the point of no-return ... We cannot allow Georgia to break up into pieces."
Saakashvili also appealed to the Kremlin to keep its troops at the base in Adjara in barracks. "A single mistake could lead to catastrophe," he warned.
Meanwhile in Batumi, Abashidze's interior minister urged people to form a human shield against any offensive by Georgian forces.
"I call on all women and children to come out on to the streets with their men and defend peace in the republic," said Jemal Gogitidze. "They are sending tanks against defenceless people."
Relations between Tbilisi and Adjara have been tense for years.
Tblisi wants wayward provinces
to recognise its authority
Abashidze runs the region like a personal fiefdom, has withheld taxes from the central government and has set up his own security force which takes orders only from him.
The crisis over Adjara was being watched closely in Western capitals - not least because Georgia is on the route of a strategic pipeline which will soon start exporting crude oil from the Caspian Sea to world markets.
In Strasbourg, the Secretary General of the Council of Europe, Walter Schwimmer, said he was "alarmed" at events in Georgia and appealed to both sides to "refrain from violence and start a genuine dialogue".
Georgia's separatist regions of Abkhazia and South Ossetia broke away from Tbilisi shortly after the Soviet Union fell apart in 1991.