A small convoy of destroyed Russian armored vehicles was towed out of the fog today around Grozny, the capital of Chechnya. Headed in the opposite direction, young Russian troops gathered around campfires here, waiting for orders to join the battle a few miles away.

The soldiers said that Russian troops are running into unexpectedly stiff resistance in Grozny and its outskirts. Three days into a Russian ground assault on the capital, troops are worried about the difficulty of crushing separatist rebels, and wishing for even more intense firepower than the almost nonstop shelling of the battered city.

"It's like the storming of Berlin. It's tough," said an officer at a nearby headquarters. "We're taking lots of casualties."

After months of pounding by Russian artillery and airstrikes--its water and electric supplies cut off, its main roads blocked by entrenched Russian forces--Grozny is not falling easily.

Russian officials, in their sketchy and inevitably upbeat reports, said the pace of the assault has been slowed by caution. They plan to take the city methodically to hold down casualties and block the escape of rebel defenders. Today, the Defense Ministry said rebels were fleeing the city, although Chechens said they were reinforcing their positions.

"You see, it's a question of tactics," said a private here named Andrei, part of a military police unit whose task is to clear rebel remnants from Grozny once federal troops have driven out the bulk of the defenders. "If we just carpet-bombed the place, turned it into an airport, we could take it in two days. But we aren't doing that, so of course there are problems."

The problems seem acute in places like Staropromyslovsky, a district just down the road that sits at the western end of a string of factories and apartment buildings about seven miles northwest of central Grozny. It would seem to be an easy target. The district, which the soldiers nicknamed the "stem of the apple," lies between ridges to the north and south. Tanks, artillery and rocket placements stand at virtual point-blank range.

Three efforts to storm Staropromyslovsky have failed, soldiers said. At one point today, five armored vehicles, some burned up, were towed from the zone. While reporters watched, a truck convoy ferried out another tracked vehicle, with a gaping hole where its front end should have been.

Staropromyslovsky is dotted with Soviet-era factories with sturdy basements, which appears to have favored the defenders. Clashes overnight took place at the Elektroinstrument factory, Chechen reports said. Even the kind of nonstop bombardment that echoed through the valley today has been unable to destroy guerrilla hide-outs, the soldiers said.

"They are like rats in holes," said one soldier. The Russians said a Chechen combat unit, called the Wolf, defends Staropromyslovsky. Among them are Ukrainian mercenaries, they said.

The Defense Ministry said, "Although the rebels put up stiff resistance and federal troops failed to kill all of them, about 50 guerrillas were eliminated." The Russians reported four fatalities of their own.

The Russians also claimed to have captured northeast sections of Grozny, with the aim of marching to the center of town. Estimates of the number of rebels in the city range from 2,000 to 5,000.

Here, in the meantime, the military police awaited their turn. Their thoughts turned to home in the days before the New Year's holiday and to ways of finding champagne so they can celebrate at the front. Some have put wills and letters home in their pockets, in case of sudden death. "I don't even tell my wife where I am. I just say I am in a rear place. She wouldn't understand," said Vladimir, a husky trooper with a green bandanna covering his scalp.

Conquering Grozny has become the major preoccupation of Russian generals, who want to avenge their expulsion from Grozny in 1996. The taking of Grozny would complete the conquest of Chechnya's plains and low hills, leaving only mountainous hide-outs to the guerrillas. Occupation would open the way for Russia to restore its rule over the vast majority of Chechens after three years of de facto independence.

Russian military officials have played down the action in Grozny since Sunday, the second day of the assault. They have directed media attention instead to the southern mountains, where rebels have retreated from the dozens of towns and hamlets that have fallen into Russian hands. "Grozny will soon be mopped up, but it is not the matter of primary concern for us," said Defense Ministry spokesman Sergei Zhuk. "The most important thing for the federal troops is the southern direction, as the majority of the rebels went there."

In Moscow, Prime Minister Vladimir Putin said simply, "The operation in Chechnya is going according to plan."

The Russians said they have begun to drop so-called fuel-air bombs over the mountains to kill the elusive guerrillas. The bombs release a cloud of inflammable gas and cause massive explosions that penetrate bunkers and caves. Given the imprecision of the bombs and their capacity to kill civilians as well as combatants, the Russians said they were using them only over sparsely populated areas.

Su-24 bombers, Su-25 jet fighters and Mi-24 helicopters took to the air today despite the low cloud cover. Over Grozny, the drone of observer planes was almost constant.

Overall, the Russians said 397 of its soldiers have died in Chechnya in the three-month ground offensive. They estimated rebel fatalities at 4,500. Chechen figures gave a radically different picture; 300 Russians have died in Staropromyslovsky alone, the Chechens said.

The exodus of refugees from Grozny has slowed markedly since the attack on the city began. Emergencies Ministry personnel said no more than 30 people have escaped through the route west into Ingushetia each day since Saturday.

People trying to reach relatives in Pervomaiskaya, between Pobedinskoye and Grozny, were turned back at the last checkpoint outside Pobedinskoye on the grounds that it was too dangerous to go farther. Proof came in the form of automatic rifle fire just 200 yards up the road. A convoy of 30 trucks was stalled, and a guard thought he saw some movement in the fields nearby. The rifle fire lasted 15 minutes and the convoy rolled away from Grozny.