A Russian general who is deputy commander of the army that has spearheaded the offensive against Chechnya was killed or captured this week while visiting a part of the Chechen capital of Grozny that the Russians claim is under their control, officials said today.

Maj. Gen. Mikhail Malofeyev of the North Caucasus army is the highest ranking officer to become a casualty in Russia's four-month-old war to pacify the breakaway region. The Chechens announced they had captured him, while Russian officials said he has been missing for two or three days and was either wounded or killed during fierce fighting in Grozny.

Russian television reports said Malofeyev was visiting soldiers and urging them to stand up and fight instead of lying down to hide from snipers. The reports, which could not be confirmed, said the general was shot in the back and head while delivering the lecture.

The incident appeared to confirm reports that, despite the Russian onslaught on Grozny, Chechen guerrilla defenders are continuing raids behind Russian lines. Russia unleashed massive air and artillery strikes on the capital again today, but refugees who escaped the bombardment said much of the battle has come down to house-to-house sniping between soldiers and Chechen rebels.

Russian soldiers said that downtown Grozny is adorned with graffiti that says, "Welcome to Hell, Part II," an apparent reference to the 1994-96 Chechen war, when rebels drove Russian forces from the capital.

The Russian advance seemed uneven. Refugees said that Moscow's forces had occupied a major bridge over the Sunzha River, but had yet to conquer Minutka Square, a major intersection and declared Russian objective. In the western neighborhood of Kirov, mine-laced streets slowed the assault.

Menacing helicopter gunships, flying in pairs, rocketed the city while jets flew above low gray clouds and punished Grozny with deafening, heavy bombing. The Russians said jets and helicopters flew 200 sorties over Chechnya today. Tank, artillery and mortar fire blasted neighborhoods throughout the city and mobile antiaircraft guns peppered apartment buildings from close range. Armored vehicles with combat-ready troops roared into outlying Grozny neighborhoods.

The defense of Grozny, along with guerrilla resistance in southern mountains, stands in the way of a Russian declaration of victory in the four-month-old war. Officials have indicated that once the capital falls and rebels are isolated in the deep south, Russia will have achieved its objectives.

The newspaper Nezavisimaya Gazeta predicted that the war will be declared over in time for the March 26 presidential election. Acting President Vladimir Putin is the favorite in that race, based largely on his promotion and prosecution of the war. The conflict, framed as a crusade against Islamic terrorists whose bombs killed nearly 300 people in apartment houses in Moscow and elsewhere last summer and who staged raids into the neighboring Russian region of Dagestan, has made him Russia's most popular politician.

"Tentatively in March, Moscow will announce the completion of the anti-terrorist operation. Otherwise, the whole election campaign would lose its logic," the newspaper said.

The battle for Grozny is taking shape in a way that, a month ago, Russian generals pledged to avoid. The Russians had planned to bombard the city with enough long-range firepower to force the rebels out before launching a full-fledged assault. Instead, Russian motorized infantry is having to move slowly into more heavily defended neighborhoods.

A Russian officer told the NTV television network that the rebels "are extremely well prepared. In our advance we have had to cross three lines of defense. As we get closer to the center, the defenses get stronger and stronger."

At a hospital in the Russian city of Perm, newly wounded troops described hellish ambushes in Grozny. A Russian sniper named Mikhail said 25 members of his unit of 70 soldiers had either been killed or wounded. The Interfax news agency said that 23 Russians died in today's fighting, an exceptionally high number.

Mikhail speculated that the rebels must be on drugs, such are their acts of risk-taking. "They go and do the job unconsciously, I think. You shoot and hit one, and he does not even fall down. This makes a big impression on the psyche, of course. Vitally important organs are hit and he does not even fall down!" Mikhail said.

Sniping and counter-sniping made escape for thousands of civilians stuck in Grozny more dangerous than ever. "You stick your head out of a building, and there's someone to blow it off," said Alei B., a 25-year-old Chechen who fled eastern Grozny before dawn.