The battle for Chechnya's ruined capital raged inconclusively into a second day, with Russian officials reporting no new advances today and setting no timetable for the fall of Grozny.

Jets and artillery pounded the city and the ground attack continued from the northwest, east and southeast. But the disparity between Russian tanks and Chechen rifles did not translate into quick Russian advances. Refugees who arrived in neighboring Ingushetia said that in Grozny's northwest neighborhoods, the movement of Russian forces was slow and rebel defenders had vowed to fight on.

Russian officials described the rebels' defense as fierce, carried out by small units roving among basement bunkers. "One must give them their due," said Maj. Gen. Vadim Timchenko, a Russian commander, speaking at Khankala, on Grozny's southeast edge. "They had built excellent defenses from the engineering point of view and turned the town into a multilayered fortress. Their fighting is, well, distinguished."

Timchenko said, however, that the rebels were running low on ammunition, food and medicine, an assertion the Russians have made several times since the ground offensive in Chechnya began almost four months ago.

Acting President Vladimir Putin, whose prosecution of the war has helped make him the favorite to win the March 26 presidential election, has said that two objectives remain in wrapping up the major part of the military campaign: the taking of Grozny and the isolation of rebels in the southern mountains. Neither event, however, would necessarily end the fighting. In the first Chechen war, from 1994 to 1996, separatist rebels continued to battle Russian forces long after the fall of Grozny and other towns and hamlets.

Nonetheless, Grozny's fall would symbolically represent a reversal of the first war's outcome, when Chechnya won virtual independence after rebels drove Russian troops from the city.

Rebel spokesmen said they expected the Russians to eventually arrive downtown--and then fall into a trap. "Real fighting in Grozny will begin only after Russian troops are drawn fully into the streets and advance to the city center," said Mumadi Saidayev, a Chechen commander.

"The Chechen military strategy does not envisage the containment of the Russian army on the outskirts of the city at any price," he said. "On the contrary, we wish armored vehicles to appear on the streets, because mobile groups, which know how to destroy armor, are ready for that."

He said eventually rebels would withdraw from the city and take up guerrilla warfare elsewhere.

This week's campaign is the second time in a month that the Russians have attempted to storm Grozny. Today, Russian forces claimed to have captured only one district, Prigorodnoye, a hamlet just beyond the eastern city limits. For the second day in a row, Russian officials announced they had seized a bridge over the Sunzha River in the center of town. They said it was a key location because rebels used it to move from one side of Grozny to the other.

Russia reported that 23 of its soldiers have died in Grozny in the past three days.

Sniping is a main rebel tool. As Sergei Chepusov, deputy commander of a motorized rifle unit, was being interviewed on television today, rifle fire broke out. "The . . . shooting you heard just then--this is shooting of enemy's snipers," he explained. "But we are suppressing it all with artillery."

Aslambek Islamilov, a Chechen commander, said fighting took place in northern and southeast sections of the city, with targets including a cannery, a dairy and a road leading north. The Russians said the cannery was under their control.

Few refugees were able to flee Grozny today, Russia's Emergencies Ministry said. One, who identified himself only as Zelim, said after arriving in Ingushetia, "There are snipers everywhere, on both sides. The fighters say they will defend the city. It is battle for every house."

In Moscow, a pro-Russia Chechen official said that Russia had opened talks with rebel commanders from the towns of Nozhai-Yurt and Gudermes, both of which are controlled by government troops. The talks were "difficult," said Malik Saidullayev, a member of the Russian-backed Chechnya Council, which Moscow created as an alternative to the separatist government of President Aslan Maskhadov.