In response, Georgian president Mikhail Saakashvili ordered police and other armed groups in Adzharia to disobey Abashidze, who has resisted his efforts to establish control over the province. He called Abashidze a "mad feudal lord."
Abashidze, meanwhile, criticized an ultimatum from Saakashvili giving him 10 days to fulfill a series of demands, saying it would not resolve the conflict.
As tensions rose, the U.S. Embassy urged Abashidze to end "violent repression," while Russia suggested it was Georgia's government that was raising worries of war.
The Georgian television network Mze said police and camouflage-clad men sprayed protesters and beat them, dispersing the morning demonstration near the main university in the Adzharian capital Batumi. It showed footage of men beating protesters, and of a man with a bloodied face and an unconscious woman being carried.
Adzharian Interior Ministry spokesman David Gergevada said police used water cannon to disperse about 200 protesters who had ignored orders to leave. He said the protest was illegal because of a state of emergency recently declared by Abashidze, and that protesters had ignored orders to break up the gathering.
Georgian Secretary Vano Merabishvili said there were "serious injuries" among the protesters. The chief doctor at Hospital No. 1 in Batumi, Dzhemal Katamadze, said three people were hospitalized with concussions and six others released after being treated for cuts on their heads.
Protester Nino Tamazashvili, a teacher at the university, told Georgia's Rustavi-2 television that unidentified men beat demonstrators while police stood by, and that 10 to 15 people were taken to the hospital. "They beat people at random: men, women," she said.
A larger group of protesters gathered in the same place later and remained into the night, calling for Abashidze to step down and chanting Saakashvili's nickname, "Misha!" Georgia's Imedi television said there were about 2,000 protesters and that they shouted down the chairman of Adzharia's government when he came to address them.
About 500 people gathered in the Adzharian city of Kobuleti to demand Abashidze's resignation, said Refat Gigidze, one of the protesters. He said they had hoped to join the demonstrators in Batumi but one of bridges between the two cities had been mined.
Abashidze said late Tuesday that Adzharian authorities would not yet take "the measures that are necessary" against the protesters but that their action would not go unpunished.
The protests came amid mounting animosity between Abashidze and Saakashvili, who issued an ultimatum Sunday giving Abashidze 10 days to disband the province's paramilitary groups, end the repression of opposition groups and accede to other demands.
Otherwise, Georgia will order new elections in Adzharia, he said.
Abashidze suggested Tuesday that he would not abide by the demands, telling the ITAR-Tass news agency that "our problems will not be solved by an ultimatum, as reality and the desires of the (central government) do not correspond. I don't need an ultimatum - I know myself what must be done in (Adzharia)."
However he left the door open to discussion, saying that he wants dialogue with Tbilisi.
Georgian Prime Minister Zurab Zhvania said on Imedi that a dialogue with Abashidze could only be about his resignation. In a televised address, Saakashvili ordered armed groups and police in Adzharia to disobey all instructions from Abashidze on enforcing the state of emergency, which he called unconstitutional.
Several Georgian television stations said that their broadcasts had been cut off in Adzharia, but an Adzharian official denied that. Abashidze accused the authorities in Tbilisi of fomenting the rally, said police were provoked and that the size of the protest showed that most Adzharians support him.
Elected in a landslide in January after leading protests that prompted the resignation of longtime Georgian President Eduard Shevardnadze, Saakashvili has vowed to unite the Caucasus Mountain nation, which was fractured when two regions - Abkhazia and South Ossetia - broke away in wars in the early 1990s.
Abashidze and Saakashvili are longtime foes, but tensions heightened in March after Saakashvili was prevented from entering Adzharia.
On Sunday, bridges linking Adzharia with the rest of Georgia were destroyed under orders from Abashidze, who said the measure was necessary to prevent an invasion by government forces. Rail connections were also broken. Saakashvili has said he does not intend to use force to bring Adzharia under control.