Russian troops moved carefully into mountain villages in Dagestan yesterday after rebels, who had held out for two weeks, said they had pulled back.
If confirmed, the rebel announcement of a withdrawal could mark an important victory for the new Prime Minister, Mr Vladimir Putin.
Mr Putin had vowed exactly two weeks ago to crush the revolt within 14 days.
Moscow was wary of declaring victory, but the worst security crisis since the 1994-1996 Chechen war appeared to be over.
"The enemy is almost defeated. There are still isolated pockets of resistance, and our forces are moving forward slowly," a spokesman for the Interior Ministry in the regional capital, Makhachkala, said.
Mr Movladi Udugov, the rebels' unofficial spokesman, said it was time Russian forces stopped shooting.
"All they are doing is continuing to destroy homes of Dagestanis. Already for a second day there has not been a single fighter in those villages," he said by telephone from the Chechen capital, Grozny.
But a spokesman for the Defence Ministry in Makhachkala said Russian federal forces did not want to move too quickly.
"At the moment it is very hard to get a clear picture. After two weeks of bombing the village of Tando, for example, has been wiped off the face of the Earth. There is nothing left of it," he said.
"The rebels there were hiding out in caves. Those were shredded by multiple rocket-launchers and caved in. How can you tell whether there is anyone inside now?"
He declined to say whether the rebels escaped, but he said at least two mass graves were found in the village of Tando alone, testifying to what he said were heavy rebel casualties.
"If they have found any dead bodies, let them show them. The only corpses they will be able to produce are the corpses of their own soldiers sprawled in the gorge," Mr Udugov said.
The rebels, led by Chechen warlords, said on Monday they had pulled out and were switching from a "purely military operation" to "military-political" tactics, an apparent sign they were ending the rebellion.
They seized villages in the province on August 7th and held out against Russian air and artillery strikes.
The rebels did not say where they had withdrawn to.