Russian warplanes attacked Chechnya's capital, Grozny, and rebel strongholds in the south of the breakaway region yesterday while voters in the rest of Russia elected a new lower house of parliament.
Russia's general staff said it had offered talks with the Chechen separatist leader, President Aslan Maskhadov, but only about the terms of a surrender.
Maria Eismont of Reuters, one of the few foreign reporters still in Grozny said the mainly elderly civilians who remained were trapped in dark cellars with little food or firewood.
Residents who escaped at the weekend to the adjacent Russian region of Ingushetia, including the border town of Nazran, said most people were afraid to leave because of heavy bombing.
Russian generals said last week they would capture Grozny within days, although they did not plan to storm it with ground troops.
On Saturday, the military said they had nearly taken control of the Chernorechiye neighbourhood in Grozny's southwest, the first district within city limits, they claimed.
Officials in Mozdok, a town outside Chechnya which is the headquarters of Russia's forces in the North Caucasus region, told Interfax news agency that warplanes and military helicopters had flown 60 sorties in the past 24 hours.
Interfax said they had struck rebel targets in Grozny, the southern villages of Vedeno and Shali and the remote Argun gorge, destroying a guerrilla base, four anti-aircraft guns, an armoured column and other infrastructure.
A Chechen rebel spokesman, Mr Movladi Udugov, said by telephone from an undisclosed location that heavy battles were raging in "practically all districts of Grozny", including Chernorechiye, where he said Russian forces had occupied the territory of a resort hotel.
Mr Udugov said his fighters had shot down two Russian helicopters ferrying supplies to paratroopers trying to seal Chechnya's mountainous southern border with the former Soviet republic of Georgia. The Russian Defence Ministry said it was not aware of losing any helicopters.
Mr Udugov also described heavy fighting near Serzhen-Yurt, a village controlling access to rebel mountain bases.
Moscow's tactics have prompted angry foreign criticism. In an interview published yesterday, the EU foreign policy co-ordinator, Mr Javier Solana, said Russia was jeopardising its relations with the West.
"We accept the fact that Moscow is protecting its territory, but not in this way," he told Germany's Welt am Sonntag. "Russia will be carelessly jeopardising its good relations with the West if it continues to wage war against its own population."
The new refugees arriving in Ingushetia painted a wretched picture of life in Grozny "There are very many people left in Grozny. There is bombing and shelling all the time, and they are scared out of their wits," said Ms Fatimat Habillata, who escaped on Saturday on a bus convoy evacuating 88 elderly and mentally ill people.
Six of the refugees had died by yesterday evening and doctors were treating others at an old people's home near Nazran.
Many of the mostly ethnic Russian old people were crying and disoriented. They said part of their residential home in Grozny had collapsed when hit by artillery shells a few days ago.
Itar-Tass news agency quoted the chief of Russia's armed forces general staff, Gen Anatoly Kvashnin, as saying military officials had met two vice-premiers and other ministers from the cabinet of Chechen leader, President Maskhadov.
"The discussions were concrete - either they fully accept what the Russian president said in his statement or not," Tass quoted Mr Kvashnin as saying early yesterday after arriving at an air base in Moscow.
President Yeltsin has demanded that the rebels surrender and turn over guerrilla leaders Moscow blames for bomb attacks on Russian cities.