The Russian warplane came droning in over the city shortly before noon today, flying above the fog and clouds that blanket Grozny like a shroud.

Suddenly, two rockets exploded simultaneously, ripping apart a man and two women at a quiet intersection in a residential neighborhood a mile from the city center. One of the women, who was elderly, was beheaded in the blast, which left blood and shrapnel on the pavement.

The Russian jet faded into the distance.

Twice in recent weeks, President Boris Yeltsin has ordered his air force to stop bombing civilian targets in Grozny, capital of the breakaway south Russian region of Chechnya.

If Yeltsin's order was meant to stop Russian warplanes from dropping conventional heavy bombs, perhaps it has been obeyed -- although there are conflicting accounts about that. But the order clearly has done nothing to prevent rocket attacks from the air, which have been put to frequent and terrifying use in recent days.

Russian forces, still trying to take control of Grozny's center, used artillery and ground- and air-launched rockets today to pummel the Presidential Palace, where the Chechen rebels are headquartered and which has come to symbolize their resistance. Heavy fighting also was reported around the railway station and several other government buildings downtown.

There were unconfirmed accounts that Russian forces had entered the presidential building and the parliament across the central square late Saturday, only to be driven back again. But Chechen militiamen fresh from the city center said the Russians had not advanced that far but were keeping up a stream of fire at the presidential building from a couple of hundred yards away.

Chechen leader Dzhokhar Dudayev was reported to be inside the building, according to the BBC, quoting a German newspaper that interviewed him. Russian news agencies reported that his son, Ovlur Dudayev, had died of wounds received in battle and was buried this weekend.

{The Reuter news service reported that the first planeload of urgent supplies from the United Nations landed in Vladikavkaz, just outside Chechnya, to help refugees from the five-week-old conflict.}

As the Russian drive to subdue Chechnya enters its sixth week, the sound of approaching Russian warplanes inspires dread in Grozny. Civilians cower in doorways, and even the toughest Chechen combatants, hard-faced men who do not flinch when an artillery shell lands nearby, go diving for shelter at the first hint of an airstrike.

Yet despite the fear caused by the warplanes, it is not clear they are having a significant military impact on the course of the war. Because of bad weather and heavy fog, Russian pilots can see little of what they are trying to hit. There are few conventional military targets in Grozny, and the ones the Russians would like to destroy are elusive.

After today's airstrikes, for example, some residents said they had seen a Chechen artillery piece known as a Zenit being driven through the area a short while before the warplane attacked. But if the Zenit was the Russian target, it was gone by the time the rockets exploded.

"They say they're fighting against illegal armed gangs here," said a woman who has stayed in Grozny. "But they're really fighting against ordinary people and houses."

The Russian attempts to storm the remaining Chechen strongholds in Grozny have been repulsed time and again since New Year's Eve, despite Moscow's immense advantages in manpower and weaponry, as well as reinforcements that have been arriving for more than a week.

Defense analysts in Moscow say the Russians already have thrown their best troops at Grozny, but the armed forces are badly debilitated by budget cuts and poor morale. There also have been reports that some elite units under the command of the Russian Interior Ministry have refused to fight in the rebel region, which declared its independence from Moscow in late 1991.

In Moscow, officials of the powerful Russian Security Council said this weekend that the war, which began Dec. 11, had entered its final stage. Yet there have been several such predictions over the past five weeks, and there was no definite sign today that the stubborn Chechen resistance was about to collapse.

"Nobody will give an inch, not even for a single day," said Magamed Abdurakhmanov, 35, a gas station attendant. "The Russians are much better equipped, with the most modern technology. But they still can't take the city."

Indeed, the Chechens still hold a sizable wedge of Grozny fanning out from the center to the south. Along a main road through that wedge, Chechen rebels race in with reinforcements and, presumably, new arms and ammunition for their countrymen fighting downtown.

From a hill overlooking the city center at a distance of about two miles, journalists watched the flash and boom of shells slamming into Chechen strongholds, including a 16-story apartment building perhaps 200 yards from the Presidential Palace. Plumes of white and black smoke were rising here and there over the city.

Hundreds of Chechen militiamen are still holed up in the 11-story presidential building -- the former Soviet Communist Party headquarters -- which the Russians have been doing their best to destroy. But it has been a difficult task: It is a massive structure with an underground bomb shelter built to withstand severe punishment.

Upper floors of the building have caught fire several times under the intense artillery, rocket and tank barrage in the last couple of weeks, most recently on Saturday. But the fires are soon extinguished or burn themselves out, and the building remains standing. While Russian troops may have reached positions directly across the square, capturing the building remains a formidable task with a high cost in casualties.

Anyone trying to cross the square on foot is apt to be caught in a torrent of small-arms fire. And, firing armor-piercing grenades from upper stories of the building, the Chechens have so far been able to make short work of Russian tanks and armored vehicles that have tried to attack.

Even if the presidential building falls to the Russians, it will likely not mean the immediate end of the war. Snipers and strong pockets of resistance may remain in the city for some time, and the Chechens have vowed to carry on a guerrilla war in the Caucasus Mountains south of Grozny if they are driven from the city.

"Even if they take Grozny, they will not be able to change our spirit, or the hatred they have cultivated here," said Zhunid Badulayev, 48, an aviation engineer.

CAPTION: Bundled against the cold, two elderly refugees trudge through the mud of Grozny toward Russian evacuation trucks.