The Information Minister, Didier Mumengi, said the two sides were fighting in the region of the border town of Bukavu in the east and around the oil town of Muanda in the west. There was no independent confirmation of the report.
Mr Mumengi, who accused Rwandan and Ugandan troops of fighting on Congolese soil, said the government launched the counter-offensive on Saturday. He said sacked Congolese army chief, James Kabare, a Rwandan, was directing the rebels.
"We launched a counter-offensive in the east and in the west yesterday. Fighting is taking place in the Bukavu region. In the west, the rebels are surrounded in Muanda and at Kitona. There is now even fighting in the Muanda area," Mr Mumengi said.
He said Rwandans on the western front, a strategic river corridor linking the capital, Kinshasa, to the sea, lacked appropriate weapons and vehicles.
Business sources said on Saturday that the Tutsi-led rebels in the west held Muanda, the garrison town of Kitona and the naval base of Banana and were reinforcing by air in Kitona. But they said there had been no reports of fighting.
Mr Kabila, who accuses Rwanda and Uganda of sending troops to fight alongside rebels from Congo's minority ethnic Tutsi community, acknowledged earlier that Bukavu and Goma in the east were in rebel hands.
Ethnic Tutsi soldiers, who spearheaded the bush war that brought Mr Kabila to power in May 1997, launched the latest revolt on 2 August in Goma, which is on the border with Rwanda.
Rwanda, whose Tutsi-led army helped propel Mr Kabila to power, and Uganda both deny involvement in the latest conflict.Reuse content