Russian forces opened a long-expected assault today on Grozny, the Chechen capital, triggering intensive firefights with Chechen defenders as Russian Interior Ministry troops and a Moscow-backed Chechen militia took the lead in advancing slowly toward the center of the besieged city.

Battles were reported underway to the south, west and east of Grozny. The Interfax news agency said explosions were being heard "almost every minute" as Russian forces laid down a heavy barrage of artillery and rocket fire ahead of the advancing troops. A Chechen commander, Aslanbek Ismailov, told Interfax that "close-in fighting" had erupted in the Chernorechnie region to the south of the city, as well as to the west, where Russian troops were approaching from a former military airport at Khankala.

The battle for Grozny has been anticipated for some time, but the Russian military held off until after the Russian parliamentary elections last Sunday. The army has insisted it will not try to storm the city, mindful of the embarrassing battles there in 1995 that led to heavy army losses and eventually to de facto independence for the Chechen region. In that light, the Russian attack now underway appeared designed as a cautious advance relying heavily on artillery support.

"I would be cautious in using the word 'storming,' " said Prime Minister Vladimir Putin's press secretary, Mikhail Kozhukhov. "The operation is developing routinely, and nothing extraordinary is happening in Grozny."

The assault was undertaken despite the presence in the capital of thousands of civilians who remain trapped in the cold, dark basements of ruined apartment buildings. By Russian estimates, about 1,500 armed Chechen rebels remain in the capital, which has been pummeled by rocket, artillery and aerial bombardment for weeks.

The battle for Grozny could have high stakes, not only in the combat zone but also in Moscow. Putin has swiftly become Russia's most popular politician as a result of his vigorous prosecution of the war over the past five months, and his future may depend on the outcome.

Trying to avoid the high casualties of the 1994-96 war, Russian forces have moved to "clean up" cities and villages only after forcing the rebels out with airstrikes and artillery fire. But in Grozny, the defenders dug in, and in entering the city, Russian troops face a far riskier and deadlier phase of the war than they have experienced to date.

Today's advance was being led by Bislan Gantimirov, a onetime mayor of Grozny who was later arrested and convicted of embezzlement in Russia. He was recently pardoned by President Boris Yeltsin and put in charge of a 500-man Russian-backed Chechen militia that was reportedly in the vanguard of the attack on Grozny.

"A methodical cleanup of the city is underway at the moment," Gantimirov told Russian television. "Only the outskirts of the city are under the control of the federal troops" at the moment, he added. "In the next few days, I think that the whole city will be under control."

The militia gained a "foothold" in southwestern parts of the city tonight, Interfax said. Gantimirov said Chechen rebels "are offering armed resistance in many areas." He said they should surrender before "the liberation of the city of Grozny" and if they do not, "their future is clear." Sketchy reports from the front said that both sides were suffering casualties, but no details were available.

"The fighting is intensifying every minute," said Movadi Udugov, a Chechen rebel leader, in an interview with Echo of Moscow radio. "We think this is a large-scale operation."

The Russian air force commander, Gen. Anatoly Kornukov, said that Gantimirov's militia "will be mainly responsible for the tasks to be carried out in Grozny." The Russian Tass news agency said the plan calls for sending in Gantimirov's men along with special Interior Ministry troops--special operations and riot control forces--while the regular army remains in the rear, attempting to seal off the city and capture any fleeing rebels.

Tass said the Russian plan is to divide Grozny into 15 sectors, take control of the city and then extricate the rebels block by block. "A structure of presence of the federal forces, which would look much like a web, will be created in the city," Tass said, adding that Russian forces hope to hoist a flag over the residence of Chechen President Aslan Maskhadov within days.

However, a pro-Russian Chechen politician, Malik Saidullayev, told Interfax that 5,000 rebels remain in Grozny and that it may take months to rout them. "No matter how much the military leaders want it, they won't capture Grozny by New Year's," he said.

The Chechen defenders remaining in the city "are beyond comparison, in terms of their combat experience and technical capabilities, to those who fought two years ago," he added. "The militants have many more weapons, modern ones included, [and] they have build fortifications around the entire perimeter of Grozny."

AUG. 7-SEPT. 16:

Chechen guerrillas supported by local militants launch attacks in western Dagestan aimed at promoting establishment of an Islamic state. Russia warns of retaliation and on Aug. 25 bombs rebel encampments in Chechnya. Russian warplanes attack Chechen villages near Dagestan, killing 45 people. Terrorist bombings in Moscow and elsewhere kill nearly 300 people. Russian officials blame Chechens and vow a harsh reprise. Russian troops also lay siege to two Islamic villages in Dagestan.

SEPT. 18-27:

Up to 30,000 Russian troops are deployed around Chechnya's borders with the stated purpose of establishing a security corridor. Moscow launches bombing raids on the Chechen capital of Grozny for the first time since the end of the Chechen war three years ago, setting off an exodus of refugees to Ingushetia. Russian troops begin a blockade of Chechnya as its planes attack oil refineries and communications facilities.

OCT. 1-NOV. 17:

Russian troops begin a ground offensive into Chechnya, occupying the northern third of the region within days and announcing the establishment of a separate administration in "liberated zones." Russian troops advance on Grozny from the west as airstrikes and shelling continue. A rocket attack on Grozny leaves 137 dead, according to Chechen officials; another rocket attack on a convoy headed out of Chechnya kills 50 refugees. The United States accuses Russia of violating the Geneva conventions with its attacks on civilians. Moscow rebuffs the criticism. Russian forces capture Bamut.

NOV. 18-DEC. 10:

Multiple Russian missile strikes on Grozny and Urus-Martan kill 170 people, and Russian troops advance from the west toward Grozny. Chechen rebels withdraw from Argun, guarding the eastern approaches to Grozny. Russian forces surround the capital. Russia warns residents to leave Grozny by Dec. 11 or face death in intensified Russian attacks. The ultimatum deadline passes. On Dec. 15 a Russian armored column enters Grozny but is trapped and ambushed by Chechens and attacked, with Western correspondents reporting more than 100 Russians killed. Russia claims to open corridors for civilians to flee, but thousands remain, hiding in cellars.

Sources: staff and news service reports.

CAPTION: Russian troops ride atop an armored personnel carrier to cross the Chechen-Ingush border not far from the village of Sleptsovskaya.