President Mikheil Saakashvili has visited the site of the gunfight that officials say has killed at least three members of Georgia's security forces and 11 Islamic militants allegedly coming from the neighboring Daghestan region of Russia.
During his visit on August 30 to the Lopota Gorge, Saakashvili vowed his government would not allow militants to move freely through Georgia.
He said the kidnapping of Georgian citizens was "unacceptable."
Earlier, officials said Georgian security forces were still searching for up to six alleged militants. Officials also said 10 Georgian hostages who had been seized by the militants were freed as a result of action by the security forces.
Saakashvili has vowed that "instability in a neighboring country will never affect" Georgia's stability.
According to Reuters, Saakashvili went on to say: "Another attempt to export a new wave of tension and instability into Georgia from our northern neighbor will be stopped at the very beginning."
Saakashvili said intelligence data showed that most of the abductors had been killed.
The Interior Ministry earlier said five Georgian soldiers had also been wounded.
It was not clear on August 30 whether the militants might still be holding Georgian security officers who might have exchanged themselves for the hostages.
Looking For Answers
The motives of the alleged hostage takers remain unclear.
Officials said two of the Georgian officers killed in the operation were security troops -- including one of Georgia's most prominent sportsmen, two-time sambo-wrestling champion Archil Chokheli. Officials said the third casualty was a military doctor.
A website associated with the Islamic insurgency in Daghestan (vdagestan.com) claimed on August 30 that the fighters in the Lopota Gorge were from what it called the "Velayat [province] of Daghestan belonging to Imarat Kavkaz [Caucasus Emirate]."
The website denied that the fighters had taken any hostages, and blamed Georgian authorities for starting the shooting that led to the fight.
The fighting in the Lopota Gorge erupted on August 28 -- the same day a female suicide bomber killed Daghestan's leading Sufi Muslim cleric, Said Afandi Atsayev, and several of his followers.
That attack prompted Daghestan's leader, Magomedsalam Magomedov, on August 30 to order local officials to create self-defense and vigilante groups to help police bolster security in the violence-torn region.
The insurgents in the region profess the extreme Wahhabi form of Islam and regularly attack police, military personnel, and moderate Muslims.
The Caucasus Emirate is a self-proclaimed entity that says it seeks to gather all Russian North Caucasus republics into one Islamic-led state. The Chechen militant Doku Umarov is considered the movement's leader.
Georgian authorities said on August 30 that troops had been sent to the border between Georgia and Daghestan to mine the area to prevent possible additional intrusions.
The violence comes amid a campaign in Georgia for parliamentary elections scheduled for October.
High tensions have surrounded Georgia's relations with Russia since the short war in August 2008 between the two countries. The war led to Russia recognizing as independent countries the Georgian separatist-controlled regions of Abkhazia and South Ossetia.
With reporting by Apsny.ge, Newsgeorgia, Reuters, AP, and Interfax