Though Moscow has not told them to, Russian generals talk of seizing the breakaway republic's capital.
Russian warplanes and artillery pummeled towns around Grozny and other parts of Chechnya on Sunday, and Chechen officials claimed at least 39 people had been killed and dozens more injured in the attacks.
The Russian military acknowledged it fired missiles at targets around the towns of Bamut and Achkoi-Martan, but said they were aimed at rebel military positions.
The bombings appear to be part of Russia's preparations for a yet unspecified second phase of the invasion. The first phase concluded more than a week ago with the Russian blitz through northern Chechnya to the Terek River. Although some Russian officials spoke of holding that line and establishing a buffer zone along the river and the western and eastern frontiers of Chechnya, Russian troops continue to advance toward Grozny, which is south of the river.
Political leaders in Moscow have stopped short of ordering a march on Grozny, yet field generals speak more openly of taking the capital. They said that Chechnya won de facto independence three years ago because skittish politicians did not let the army do its job.
One television station broadcast interviews with infantrymen who pledged to "finish off" the Chechens. "Everything will be okay if we are not hindered," said one.
"If we are pulled back," warned another, "they (the Chechens) will regain their strength and this muddle will begin again."
Chechen leaders meanwhile again called for peace talks with Russia, demanding they be held on neutral territory with international mediation.
"The conditions for the peace talks are a cease-fire and the withdrawal of Russian troops from Chechnya, or Russia's complete capitulation," Chechen Vice President Vakha Arsanov told the Associated Press.
The Chechen military reported that the Russians "heavily pounded" villages to the north and east of the capital, Grozny. It said that a pre-dawn Russian rocket attack on the town of Vedeno, 18 miles southeast of the capital, had killed 23 people and wounded 58.
Russian artillery also targeted the village of Samashki, near Chechnya's western border, killing 16 people and wounding 41 others, the Chechens said.
The casualty figures could not be confirmed, and the Russian command did not offer any estimates of its own. It stressed that the attacks were aimed at militants rather than civilians.
The Chechens did not say if the casualties included rebel fighters.
"The militants are strengthening their positions," said Col. Gennady Alyokhin, a Russian military spokesman, and Russian troops are responding with "some artillery strikes against the rebels' bases."
The Chechen military command claimed its fighters downed an Il-20 Russian reconnaissance plane overnight with a Stinger missile, after shooting down two warplanes Saturday. The Russian air force vehemently denied losing any of its planes in recent days.
Grozny was calm Sunday, though most people ventured out of basement bomb shelters only to cook food on campfires in the streets. Electricity and gas in the city have been shut off.
Some residents shopped for food at the city's central open-air market, which reopened Sunday after a Thursday night bombing that killed at least 143 people. But they didn't linger, fearing Russian attacks.
A group of Russian leaders from regions surrounding Chechnya pressed for negotiations to end the fighting.
Ruslan Aushev, the president of neighboring Ingushetia, said that the leaders had met Saturday and called for Aslan Maskhadov, the Chechen president, to meet with Russian President Boris Yeltsin or with Prime Minister Vladimir Putin, the Interfax news agency reported.
Russian officials have repeatedly balked at suggestions for negotiations, saying the war is aimed against terrorists. Russia sent troops into Chechnya at the end of September, ostensibly to wipe out militants who invaded neighboring Dagestan this summer and were blamed for a series of apartment explosions in Russia that killed some 300 people.
But the Russian offensive increasingly appears aimed at restoring Russian control over Chechnya.
Aushev said that some 169,700 Chechens had taken shelter in Ingushetia, and that the republic was "suffocating under such a tide of refugees," Interfax reported.
_ Information from the Washington Post was used in this report.