Russia's NTV television said the rebels had unsuccessfully tried to cross into Chechnya during the night.
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It is reported that they had previously been hiding in the Pankisi Gorge in northern Georgia, until Georgian forces began an operation to flush them out.
Russian Defence Minister Sergei Ivanov told President Vladimir Putin that the group of 180 had not been completely destroyed.
Other officials said three fighters who had been taken captive said they crossed into Ingushetia on 1 September.
During the fighting on Thursday they shot down a Russian helicopter with a portable missile launcher, killing the crew of two.
A military spokesman said on Friday that helicopter gunships were now being used "cautiously".
Casualties
The number of casualties is unclear, with one Russian report of 70 dead in Galashki, where the helicopter was shot down, and a similar number in other areas where clashes took place.
Among the dead was a British news television reporter, 31-year-old Roddy Scott.
Georgian Foreign Minister Irakli Menagharishvili said Georgia was not responsible for the events in Chechnya.
"The Pankisi Gorge operation is intended to ensure that there are no potential threats to Russia from Georgian territory. We have assumed this commitment and will meet
it."
Russia has threatened to attack Chechen rebels on Georgian territory, unless Georgia does the job itself.
Georgia points out that Russia drove the rebels across the border in the first place, and says its main aim is to drive them back.
Thursday's fighting was the heaviest seen in Ingushetia in the last three years of conflict.