Despite the increased troop presence, some rebels appeared to be holding out in Komsomolskoye, which they seized from Russian hands last Sunday. The raid embarrassed the Russian command, which claims to control most of the breakaway republic.
The tanks moved into Komsomolskoye on Saturday after a fresh snowfall, followed by units of infantry on foot and in armored personnel carriers. Russian aircraft scaled back their bombing of the town Saturday, but artillery fire remained heavy.
Six days of bombing and shelling have razed or damaged nearly every house in town.
The military command said up to 700 militants were still in Komsomolskoye, and were suffering heavy losses. Officers in Alkhazurovo, a village about a half-mile away, said rebel numbers were considerably smaller.
The Interfax news agency reported Saturday that a large group of rebels had tried to break out of town, but were "scattered" by Russian forces. The Russians are apparently trying to trap the rebels in town to keep them from escaping south to join comrades in the mountains.
The resistance was reportedly being orchestrated by two of Chechnya's most notorious warlords, Shamil Basayev and Khattab, who uses one name only. But the two were not believed to be in Komsomolskoye.
Russian troops have focused their offensive in Chechnya's southern mountains since thousands of rebels abandoned Grozny last month. Russia has been unable to rout the militants after six months of war, even though Russian troops outnumber them and have superior weapons.
Russian news reports said Saturday that a large group of rebels had broken out of bases in the Argun Gorge, moved southeast through the villages of Ulus-Kert and Selmentauzen, and reached rebel bases in the Vedeno region.
Ulus-Kert and Selmentauzen have seen some of the heaviest fighting in Chechnya in recent weeks.
Commanders want to block rebels from launching attacks in Russian-held flatland areas. Such attacks have already caused heavy Russian losses.
Meanwhile, a delegation from the Council of Europe visited the shattered Chechen capital, Grozny, and a detention camp where human rights groups allege Russian troops have tortured inmates.
The nine-member delegation is investigating the allegations to help determine whether to suspend Russia's membership in the council, the continent's leading human rights body. Western nations have criticized the offensive in Chechnya, citing civilian casualties and rights abuses.
Lord Judd, head of the delegation, said he was shocked at the devastation in Grozny. Bombed-out or flattened buildings dominate the once-bustling city, and its few thousand remaining civilians are mostly holed up in basements.
"It seems to me terrible that at the beginning of the 21st century, on the continent of Europe itself, you can see large-scale destruction and consequent suffering," Judd said.
In St. Petersburg on Saturday, Russia's acting President Vladimir Putin told visiting British Prime Minister Tony Blair that he would consider changes in Moscow's policy on Chechnya, based on Blair's concerns about allegations of rights abuses. Putin did not name what the changes could be.