"We took Shabunda on Wednesday and it is now under our total control. Fighting is also taking place in Isiro where our forces have arrived," he said.
He said the rebels were moving on a large airfield near the town of Kindu, others had reached Isiro in the north-east, where heavy fighting was raging, and a third group was advancing on Moba in the south-east.
Mr Kabila said some of the 300 mercenaries hired by the government to crush the eastern revolt were based in Isiro.
Rebel officers said the 5,000 newly trained rebels would be dispatched to join their comrades advancing on four fronts against government forces.
Church sources and aid workers said earlier that the rebels had captured the eastern town of Shabunda and were advancing towards Kindu, which has an army base and an airport and was a springboard for a government army counter-offensive launched last month. The rebels, who frustrated the offensive by opening up new fronts, were moving in large numbers towards Kindu, 120 miles to the west, Church sources added.
"The fall of Isiro is a matter of hours," a senior rebel commander said. Isiro is about 300 miles north-west of Goma, which fell to the rebels last year.
Life came to a standstill in Goma as many of its 300,000 residents lined a six-mile route from the airport to the city centre to cheer the rebels, who were addressed by Mr Kabila. Dressed in new combat fatigues, the recruits sang battle songs praising Mr Kabila and denouncing Zaire's President, Mobutu Sese Seko.
An official of Zaire's state-run mineral mining company, Gecamines, said he saw no immediate danger from the rebel advance and hoped a deal would soon be signed with a South African company.
The rebels have advanced into the south-eastern region of Shaba to Kalemie, 500 miles north-east of Lubumbashi.
Mr Kabila's radio station in Goma broadcast an appeal to King Hassan of Morocco not to provide military aid to Mr Mobutu, who is visiting his long-time ally.
The Zairean leader is in Morocco on his way home from France where he has been convalescing from prostate cancer surgery. Moroccan troops in 1977 helped to put down a secessionist uprising in Shaba after Zairean forces failed to make headway.
nRuhinga, Burundi, (Reuter) - Disease has killed 150 Burundian Hutus grouped by government troops into a relocation camp at Ruhinga north of Bujumbura, occupants said yesterday. They said bacterial dysentery, diarrhoea and malaria were rampant in the camp.