Russian military forces poured artillery, mortar and machine-gun fire through the fog at Grozny today but appeared to make little progress in the second day of their long-anticipated ground assault on the Chechen capital.

The seizure of Grozny now seems a primary objective of the Russian offensive in the separatist southern region, but one that stirs up bitter memories. On New Year's Eve 1994, Russian ground forces suffered heavy losses as they tried to storm the city and suppress a Chechen drive for independence from Moscow. The Russians finally took Grozny the following spring but were subsequently driven out of Chechnya in a two-year conflict with rebel forces that left the region virtually autonomous.

This time, military officials have insisted they will be more deliberate in their advance on Grozny to avoid the confusion and casualties of five years ago. In that assault, columns of tanks and other armored vehicles penetrated deep into the city center, where they were cut off by the Chechen defenders and became easy prey to guerrilla tactics and shoulder-fired antitank weapons.

There can be little doubt now that Russian commanders intend to capture Grozny soon. Roads into the city from the east and west are filled with armored vehicles and trucks making their way toward the front, according to witnesses on Grozny's outskirts. But the Russian military commander in Chechnya, Gen. Victor Kazantsev, played down expectations of an immediate breakthrough, telling reporters: "Nothing terrible is happening in Grozny; all that's going on is a continuation of the operation to free the city of bandits. Let's not hurry, but you'll soon see."

A Chechen ally of Moscow, former Grozny mayor Bislan Gantamirov, was more upbeat, saying militia forces under his command would raise the Russian flag in central Grozny by Dec. 31. Gantamirov said his forces had already reached a neighborhood in the city center, but Russian officials who visited the front today said it was unlikely Gantamirov could keep to his timetable.

Meanwhile, fighting apparently raged in and around the city all day, as Russian forces probed Grozny neighborhoods and pounded rebel positions with artillery fire and airstrikes. Russian officials said troops were braving sniper fire and the threat of land mines as they moved gingerly through the warren of simple houses and mid-rise apartment buildings that make up much of Grozny. A report on state-run television said some troops had reached the Minutka square, near the city center, but it was unclear if they remained there.

Russian officials did not claim to occupy any district in Grozny, and video footage taken from one suburb--Chernorechnye, on the south side of the city--showed rubble-filled streets and other heavy damage, but no sign that Russian forces had taken control.

Spokesmen for the Chechen defenders claimed their forces were returning fire with mortars and machine guns, inflicting casualties and destroying Russian equipment. "Fighting is raging; everything that moves is destroyed, and the city is covered by all types of weapons," Movladi Udugov, a Chechen official, said on a Moscow radio station.

The Interfax news agency said the heaviest combat appeared to be taking place on the outskirts of Grozny as Russian forces attempt to drive the rebels back into the center of the city. The army's tactics seem to be to send out reconnaissance units, draw rebel fire, then pound Chechen positions with artillery. An undetermined number of civilians--Chechen officials say tens of thousands; Moscow says hundreds--remain in the city, and the Russian Emergencies Ministry said that the heavy shelling prevented many from fleeing today.

Besides agreeing on the scale of the Russian bombardment, Chechen and Russian reports coincided on one other matter--the Chechen rebels are trying to send reinforcements into Grozny. The Russians said they have blocked these attempts, while the Chechens said fresh forces have succeeded in reaching the capital. It is virtually impossible to verify all such claims; Russian forces have sealed all entrances to Chechnya, and reports of Russian journalists traveling with the forces are sketchy.

A videotape shown on Russia's independent NTV channel showed army artillery batteries and recoilless rifles pouring fire on Chechen positions. The Russian troops were entrenched in fields and woods, suggesting that these soldiers, described as a front-line unit, were still outside Grozny.

The troops had converted an empty oil tank into a mess hall and were entertaining themselves with cassettes of Chechen music. But danger was not far away, especially after sundown. "There is a rain of lead here, at night," one young soldier said.

The Chechens facing them are holed up about a mile away in concrete-reinforced trenches as deep as 15 feet. The soldiers said the Chechens yell at them at night--"Ivan, surrender"--and walk around "in the open, like they own the place."

The Chechens' immediate intentions are unclear. Spokesmen said they intend to keep defending the capital, but their strategy during the earlier war--and in some towns during this one--has been to withdraw under Russian pressure to mountain strongholds in the south.

Shamil Basayev--a Chechen guerrilla leader who played a key role in the conflict five years ago--has said Russian troops will not take Grozny. "They are only fighting for money," he said. "I will not negotiate now because there is not a third party or any guarantees from the international community. With Russians it's impossible to make a deal. Only fighting works."

A video report from Grozny, recorded between Dec. 5 and Dec. 17, showed Chechen rebels holed up in apartment buildings and basements, while the main streets appeared deserted. One guerrilla said the defenders will stay in the city, "as long as we want . . . as long as possible."

A hint of the sort of determined resistance Russian forces might expect came with reports that saboteurs had tried to blow up two stretches of railroad tracks in Russian-occupied northern Chechnya. Russian demolition experts defused the explosives, but came under sniper fire as they did so, the reports said. The episode served as a reminder that, after Russian troops captured Grozny in the earlier war, they remained subject to guerrilla harassment and were eventually driven from the city by a massive rebel ambush.

CAPTION: Russian troops on the outskirts of Grozny load the bodies of Chechen guerrillas onto an army truck.