Russian spokesmen later said fog prevented the military from defending the original column, but the survivors say the weather was clear much of the time.
A Russian military spokesman called the situation "totally out of control."
Those reports have been vigorously denied by Russian military spokesmen.
Russian military spokesmen put Russia's losses at 59 dead, while reporting that more than 1,000 rebels had been killed.
Russian military spokesman insisted that rebel casualties have been far greater, but there was no way to confirm that.
A Russian spokesman said it reflected "the politics of double standards, known from the period of the cold war."
According to a Russian military spokesman, 17 Chechens and at least one soldier were killed in the operation.
Russian military spokesmen said their forces were making slow but steady progress.
Tonight, a Russian spokesman said the military could not shell the militants in the town without endangering the civilians.
A Russian military spokesman said that special forces bombed the market because it was actually an arms bazaar.