The ministry said five soldiers also were wounded near the frontier with Russia's Dagestan region, but did not give the nationality of the gunmen or say whether they had entered the country from Russia.
If the gunmen turn out to be from Russia, the incident could increase tension between Moscow and pro-Western Tbilisi, whose relations are still strained following a five-day war in August 2008 over two Russian-backed separatist regions in Georgia (see background).
"Another attempt to export a new wave of tension and instability into Georgia from our northern neighbour will be stopped at the very beginning," Georgia's President Mikheil Saakashvili said in a televised statement.
Saakashvili said intelligence data showed that most of the militants were killed.
Michael Mann, spokesperson to High Representative Catherine Ashton, said today (30 August) the EU was “very worried” and regretted that the incident took human lives. He said the mandate of the EU observer mission to Georgia did not cover the area of the incident, and that no observers had been dispatched there.
“For the time being, we are trying to see with the [Georgian] authorities what exactly happened,” he said.
Asked if the Commission saw the incident as related to the forthcoming elections in Georgia, Mann said he could not speculate.
Georgia had sent troops to the region in the north of the country on Tuesday to help local police release several hostages. An unspecified number of hostages had been freed and there was at least one exchange of gunfire during the operation, an Interior Ministry spokeswoman said.
On Wednesday, troops surrounded six militants in a Caucasus Mountain gorge.
On Tuesday, residents of Lapankuri, a village 30 km from the border, told Georgia's Rustavi-2 television they were concerned because five neighbours had been missing for days and they had seen men who appeared to be from Dagestan in the area.
Rustavi-2 later reported that gunmen had taken three groups of people hostage in the northern Kakheti region.
Border post shooting
Footage released by the Interior Ministry showed a resident of Lapankuri, Levan Khutsarauli, who said several bearded men took him and other villagers hostage.
"They warned us that they would kill us if we only tried to run away," Khutsarauli said. Media access to the area of fighting has been restricted by the authorities.
It was unclear whether there could have been any link with a shooting at a Russian border post in Dagestan late on Tuesday in which authorities said a border guard killed seven fellow servicemen before being shot.
Insurgents fighting to carve an Islamic state from the North Caucasus attack Russian officials and law enforcement personnel almost daily, and have also increasingly targeted mainstream Muslim leaders who are backed by the authorities.
It was not clear why militants in Dagestan might cross the border into the neighbouring former Soviet republic and seize hostages.
A spokesman for Russia's FSB security service, Vadim Shibayev, told RIA news agency that there were no registered cases of violation of the Russian-Georgian border.
Russia sent troops into Georgia in August 2008, repelling a Georgian offensive aimed at gaining control of separatist South Ossetia, which has run its own affairs with Moscow's support for 20 years.
The conflict also enveloped breakaway Abkhazia. Moscow recognised Abkhazia and South Ossetia as independent countries following the war and increased its military presence in the regions, drawing criticism from the United States and NATO.
Georgia, which holds a parliamentary election on 1 October, and Russia still have no diplomatic relations and communicate through Swiss diplomats.