Russian forces patrol the city, where snipers and car bombs continue to claim lives.
Russian forces have mounted numerous security operations and reported foiling intended attacks by Islamist militants.
Fighting that started last week has died down in the region, but Russian forces remain.
Military specialists say there is no easy option for the Russian forces converging on Grozny.
Abuses by Russian forces stationed in Chechnya have continued to act as a recruiting sergeant for the rebels.
In battle the hastily cobbled- together Russian forces there have, to date, been no match for the Chechen irregulars.
One such area is the town of Akhalgori, which puts the capital, Tbilisi, within easy reach of the Russian forces.
Meanwhile, South Ossetia's capital, Tskhinvali, lay in smoldering ruins Sunday after three days of fighting between Georgian and Russian forces.
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He visited South Ossetia and introduced a new law that makes it easier to deploy Russian forces outside the country.
By mid-week, Russian forces had taken up positions along the Terek river, and some were within artillery range of Grozny.
The biggest Russian forces outside the regular army are the interior-ministry troops, numbering about 250, 000, and about 200, 000 border guards.
Chechnya, where the Tsarnaev family has roots, has been the scene of two wars between Russian forces and separatists since 1994.
He escaped from Stalag Luft 3 POW camp in Poland and was rounded up by the Russian forces when hostilities ceased.
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Many believe that he walked into a trap, miscalculating that he could take South Ossetia before Russian forces arrived in strength.
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Nato states are first demanding the withdrawal of Russian forces from Georgia and Moldova, but Moscow says the issues are not linked.
Several residents said they worried that Russian forces would attack Tbilisi.
From what outsiders can gather, the performance of Russian forces was patchy.
Observers say the Chechen counter-offensive has dealt a stunning blow to the Russian forces, and that the rebels appear to hold the initiative.
He also challenged Khalilzad's argument that Russian forces were waging a "campaign of terror" there, essentially telling council members to consider the source.
Russia ratified the revised version, but Nato states have not done so, first demanding the withdrawal of Russian forces from Georgia and Moldova.
Since then, though Russian forces have remained in nominal control of the region, they have continued to suffer heavy losses from rebel attacks.
Georgia, meanwhile, has accused Russian forces of several times infringing Georgian territory in its attempts to seal the mountainous border between Georgia and Chechnya.
After beating a humiliating retreat in 1996, Russian forces were sent back in 1999, following a rebel raid on the southern Russian region of Dagestan.
Many dozens were reported dead, including militants, civilians and Russian forces.
During the Abkhazia conflict, which began in 1992, the year after Georgia gained independence, there were numerous reliable reports of Russian forces assisting the Abkhaz separatists.
As well as claiming to have surrounded Grozny, the capital, Russian forces say they have encircled Chechnya's second town, Gudermes, cutting off the Chechen fighters there.
He claimed up to 150 Chechen fighters had been killed in Shali and up to 100 others wounded, while Russian forces had now "completely cut off" Argun.
Now, after more than four years of Mr Putin's second attempt at crushing the rebellion, the body count among Russian forces is approaching that of the first invasion.
The United States boycotted preparatory meetings Tuesday for a NATO meeting with Russia, and NATO has canceled a naval exercise with Russian forces in the northern Pacific.
Khalilzad said the United States plans to offer a draft resolution calling for an immediate cease-fire in Georgia, accusing Russian forces of impeding the withdrawal of Georgian troops from the territory.
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