Chechen rebels launched a rare counterattack westward from the capital of Grozny against Russian troops besieging the city, and the Russians struggled to contain them.

Reports reached Moscow of increasing Russian casualties, with soldiers complaining that the assault on the city is uncoordinated and that hospitals are filling up with the wounded.

Grozny has been under sustained ground attack for almost two weeks, an onslaught backed by nearly continuous airstrikes and artillery fire.

The rebels have put up stiff resistance, blocking their foes at the city's edge. Russian Interior Ministry forces have probed Chechen defenses from all directions, and claim to have captured at least one neighborhood, Staropromyslovsky, in the northwest. Other recent claims of advances have proved optimistic and have been dropped from official reports.

Today, for the first time, the Chechens launched an attack westward from Grozny to an area occupied by the Russians for more than a month: the towns of Alkhan-Kala and Alkhan-Yurt. "Combat activities continue in the Alkhan-Kala district," said Vasily Chirman, a commander at the Russian Caucasus military headquarters in Mozdok. "We have been destroying a group that made an attempt to break out."

ORT, a state-run television station, said that rebels were surrounded in Alkhan-Yurt and "will be destroyed."

Chechen officials said fighters reclaimed three towns--Alkhan-Kala, Alkhan-Yurt and Kurali. The three form a triangle to the southwest of Grozny. Rebel spokesman Movladi Udugov said attackers destroyed the headquarters of Gen. Vladimir Shamanov, the western front commander. There was no way of verifying Udugov's claim, which the Russians denied.

The significance of the rebels' thrust westward is that it marks not an attempt to flee Grozny and head south to the mountains, but an effort to inflict casualties and cause havoc behind Russian lines. Chechens have mounted small ambushes in areas of Chechnya controlled by the Russians, but nothing that the Russians had characterized as coordinated combat.

The storming of Grozny is taking longer to complete than Russian officials had predicted at various times. Over the weekend, acting Russian President Vladimir Putin put a stop to speculation about a timetable by saying no date has been set for victory.

Occupation of the battered capital would place Russia in control of the most heavily populated parts of Chechnya, and perhaps mark the zenith of its offensive. If the 1994-1996 Chechnya war, in which the Chechens won de facto independence, is any guide, the war could turn into a prolonged guerrilla conflict.

Trying to enter Grozny this time, the Russians have run into constant sniper fire and ambushes. Snipers "almost never miss the target," said Lt. Konstantin Kukhonovets, a platoon commander. In Staropromyslovsky, soldiers complained to television crews that reports about control of the district are false. "Soldiers are killed by the dozen . . . We are hit by our own mortar fire," complained one.

Today, the rebels also attacked Russian forces along the Argun Gorge and the road that leads south to Georgia. Russian officials denied Chechen claims of having routed their forces from parts of the road. However, soldiers in the foothill village of Avtury said they were vulnerable to frequent mortar attacks and rebel incursions. "They try to sneak in here. We caught one only 10 meters away from our positions, but he had time to throw a grenade into an armored personal vehicle," said one soldier in a televised broadcast. "He wanted to run away, but couldn't. That's his problem."

In a foretaste of another tactic that may bedevil the Russians in the future, a hidden bomb exploded as five army vehicles traveled by on a road in Dagestan, the region east of Chechnya. No soldiers were hurt, a Russian statement said.

Abroad, Russia is also vulnerable. A Palestinian fired four rocket-propelled grenades at the Russian Embassy in Beirut today. No Russians were hurt, although a Lebanese policeman was killed in the ensuing shootout. The Palestinian was gunned down by Lebanese troops and police. A note in the pocket of the attacker, Ahmed Abu Kharub, said, "I martyred myself for Grozny."

The Russian government issued no casualty reports from Chechnya today, but recently official numbers have indicated death tolls of 10 a day. Over the weekend, a group of soldiers at the front complained of slow medical service. They said a comrade of theirs died on the operating table at a field hospital--the second from their unit. "That's a lot for us," one of the angry soldiers said.

CAPTION: A Chechen woman stands in a village heavily damaged by Russian bombs and artillery fire.