The Georgian president has declared direct presidential rule over Ajaria, saying the end of rebel rule in the province is only "hours" away.
Abashidze's police force has been defecting to the Georgian side
Mikhail Saakashvili offered Ajaria's long-standing leader, Aslan Abashidze, safe passage abroad as a Russian envoy began talks to broker a settlement.
Mr Abashidze has said he has "no intention of leaving".
He is still backed by an armed militia despite large rallies against his rule in the provincial capital Batumi.
Mr Abashidze has challenged the authority of Georgia's new president in a stand-off which has aroused the concern of Russia, Europe and the US, all of whom consider the Black Sea state to be of key strategic importance.
One unconfirmed report said a small number of Georgian troops had been dropped by helicopter inside Ajaria but there was no indication of any violence.
An unnamed security official in Mr Abashidze's administration told AFP news agency that about 200 militia had surrounded the troops near Shakvi, a village about 20km (12 miles) from Batumi.
Russian Security Council Secretary Igor Ivanov flew into Ajaria and was met by Mr Abashidze in person before being whisked off for talks, reportedly also involving Georgian Prime Minister Zurab Zhvania.
News of Mr Zhvania's arrival in Ajaria delighted thousands of demonstrators in Batumi who have now been joined by local police officers.
Population: 400,000; overall population of Georgia: 5 million
Depends on income from transited goods, its port shipping about 200,000 barrels of oil a day
Has run its own affairs for years, withholding tax payments from central government in Tbilisi
Ajarians are ethnic Georgians but mostly Muslim, unlike the majority in the Orthodox Christian state
Echoing last year's revolution against Georgian President Eduard Shevardnadze, they waved red roses and chanted "Misha, Misha" - President Saakashvili's nickname.
However, before Wednesday's talks, Mr Abashidze, 65, said he meant to stay in Ajaria and that there was no "basis for confrontation".
He insisted that he had been "democratically elected by hundreds of thousands of people" while those protesting against him numbered, he said, only about 5,000. Reporters put the number between 7,000 and 10,000.
Mr Abashidze's men have said they will open fire if demonstrators move closer to their leader's residence.
The rebel leader, who maintains strong links with Russia, strongly opposes the Western-leaning President Saakashvili, who swept to power after staging peaceful protests last year.
'End of the regime'
"I am introducing direct presidential rule in Ajaria for a transitional period," Mr Saakashvili announced in a televised address on Wednesday.
A provisional council, he said, would be set up to govern the province before local elections could be held and he offered safe passage to Mr Abashidze if he resigned and left the country.
Several thousand have taken to the streets to call for Abashidze to go
Georgian Security Council Secretary Vano Merabishvili warned that Mr Abashidze's militia had to lay down its arms "within hours" to avoid blood being spilled.
"The hours of Aslan Abashidze's regime are numbered..." he said on TV.
The Georgian government on Sunday issued a 10-day ultimatum for Mr Abashidze's militia to disarm.
The US is backing the construction of a multi-billion dollar pipeline to transport Caspian Sea oil through the volatile region to the international market.
The US State Department called on Wednesday for a "political dialogue" to resolve the crisis.