Russian tanks blasted rapid-fire barrages into Grozny today from hills on the edge of Chechnya's capital, working to drive out rebels as Russian ground forces gingerly advanced toward the city center.

The military claimed to have broken through the rebels' first line of defense in Grozny, and to have taken control of the Staropromyslovsky neighborhood about two miles from the city's center, but there were no signs Russian forces were advancing quickly.

A rebel leader said his fighters were standing firm.

"Federal troops have not advanced by a single meter," said Khamzat Gilayev, commander of the units defending Grozny.

A line of about 25 tanks in the hills above Staropromyslovsky fired on the city in rapid succession. Meanwhile, civilians cowered in basements, where many of them have hidden for weeks with meager food supplies. One family showed a reporter a larder bare of anything but a jar of fruit.

Russia invaded Chechnya in September, aiming to wipe out Islamic militants who staged an armed incursion into neighboring Dagestan this summer. Russian authorities also have blamed Chechens for a series of apartment house bombings that killed nearly 300 people in Moscow and elsewhere around Russia.

Russia's strategy toward the breakaway region appeared unchanged in the wake of President Boris Yeltsin's surprise resignation today. Prime Minister Vladimir Putin, Russia's acting president, has championed the war and vigorously defended Russia against Western criticism of the offensive.

After months of bombing and shelling the capital, the Russians launched an operation on Christmas day to capture Grozny, the last major Chechen city under rebel control and the war's foremost political prize. But Russian forces have been held up by heavily mined roads and tough rebel resistance.

Groups of 10 to 15 guerrillas moved swiftly through the city today, firing from prearranged positions. The Russian troops were trying to avoid head-on clashes with the guerrillas, who challenge Russia's superior manpower and weaponry with formidable street-fighting skills, the Interfax news agency cited military sources as saying.

Russian forces also were fighting to isolate rebels in the rugged mountains of Chechnya's southern border with Georgia. In the narrow passes and gorges of the region, Russian troops are vulnerable to guerrilla attacks, and they have moved slowly into the fog-shrouded terrain.

Both sides said they were expecting large-scale fighting over the New Year's holiday, with the Chechens hoping to catch celebrating Russian soldiers by surprise. Russian Interior Ministry troops have been ordered to strengthen protection of their bases.