Dudayev, president of the self-declared Chechen republic, had earlier sent hundreds of his men storming into the town of Urus-Martan, south of the capital Grozny.
His officials later said the town, a key base of the Moscow-backed opposition, had been captured by government forces by 1 P.M.
"At the moment, bodies are being collected and those armed opposition forces who managed to get away are being hunted," Itar-Tass quoted an Interior Ministry official as saying.
Interfax said some 30 tanks and armored vehicles with about 2,000 fighters took part in the offensive on Dudayev's side. The opposition, according to the agency, had several hundred fighters and 20 pieces of armor.
The attack on the base, where the splintering opposition has concentrated most of its forces to attack Grozny, may deal a sharp blow to rebels' plans to topple Dudayev soon.
Urus-Martan is the main base of anti-Dudayev fighters under the leadership of Bislan Gantemirov.
At least 15 bodies could be seen in Urus-Martan's central street, with walls pitted by bullet marks and some buildings damaged by shells. It was not clear whether these victims were government soldiers or opposition fighters.
A local hospital doctor said 44 people had been brought in with serious wounds, 10 of whom had died later.
Interfax said a hospital in the village of Znamenskoye, opposition headquarters on the border with Russia, was filled with wounded. There were no reports that Znamenskoye was attacked.
Shooting still echoed throughout the town in mid-afternoon, but Dudayev's military commanders said this was because opposition fighters were still being flushed out.
Itar-Tass said Dudayev's forces started massing around Tolstoi-Yurt, powerbase of former Russian parliament speaker Ruslan Khasbulatov, an ethnic Chechen and one of the anti-Dudayev opposition leaders.
Dudayev's offensive followed a surprise opposition attack on Grozny last week in which its units, supported by military helicopters, seized several city suburbs.
The opposition later withdrew its forces to Urus-Martan with Gantemirov saying Saturday's attack was just a training run. Dudayev hailed it as a victory for his forces.
The fractured Chechen opposition has received Moscow's explicit backing in its attempts to oust Dudayev, a former Soviet air-force general who has led his republic of 1 million people on a path of unilateral independence from Russia.
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