Dudayev coupled his proposal with an appeal for a simultaneous Russian troop withdrawal which Moscow has previously rejected. Meanwhile Chechen fighters reinforced their position on the outskirts of the ravaged capital, Russian reports said.
Postfactum news agency said Dudayev had asked Russia "to cease military activity from 8 p.m. on Dec. 31 and start the removal of troops, in connection with the dawning of the new year and with the aim of preventing further senseless bloodshed."
There was no immediate response from Moscow.
The Russian government press service reported a major clash between Russian troops and Chechen fighters overnight on the edge of Grozny.
In the center of the capital, the presidential palace still stood untouched while the ruin of bombed buildings lay around it. Thousands of remaining residents were essentially trapped in the city, unable to find transport to get out and afraid to run the gauntlet of death to escape on foot. "It's just me and my son, we're all alone," said Lyudmila Dmitrova, one of hundreds of ethnic Russians who have nowhere to go.
Chechnya's parliament circulated an appeal to world leaders calling for pressure to be exerted on the Russian leadership and for aid to prevent a possible ecological catastrophe as the result of fires at burning oil facilities in Grozny.
The appeal came as smoke continued to billow from a bombed-out Grozny refinery. The fire threatened to ignite a tank of deadly ammonia nearby, officials said.
Russia blamed the refinery fire on Chechen mines, not the virtually nonstop Russian airstrikes pounding Grozny. "None of the refineries have been bombed or shelled," the press service said.
An ecumenical group of clerics from the Caucasus region, meanwhile, met in the southern Russian city of Vladikavkaz and issued a statement calling for peace in Chechnya.
The clerics also called on people to help refugees, Itar-Tass reported.
An estimated 100,000 people have fled the fighting. Russian military officials were quoted by Moscow media as saying their forces had occupied Grozny's Khankala airport and the settlement of Oktyabrskoye southwest of the Chechen capital. Previous reports had said the Russians captured the airfield earlier this week.
The Russian army has dealt punishing attacks on the Grozny environs this week, bombing factories in the capital, shelling villages and entrenching their positions amid heavy fighting on the city's fringes. Their offensive to restore Russian authority to secessionist Chechnya was in its 19th day; Russian Defense Minister Pavel Grachev once said it would take only two hours.
International unease over the bloody offensive is growing.
Thursday saw some of the heaviest action yet in the offensive, which is aimed at ousting the Dudayev regime and putting down the southern republic's three-year-old independence bid.
The Russians claimed to have destroyed Dudayev's personal helicopter and one aerial bomb just missed the presidential palace, devastating a nearby house. Dudayev and his entourage have moved their offices to the basement of the building.
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