Gunfire was reported in the eastern town of Bukavu near the border with Rwanda, said aid workers based there. A provincial official said that the rebels were in control of the town, although some reports indicated fighting there continued.
Banyamulenge Tutsis and Rwandan soldiers led the uprising against Kabila, accusing him of widespread corruption and government mismanagement.
In the southwestern village of Kitona, where rebel gunmen forced a hijacked private airplane to land, fighting was reported at the town's main military base, a government spokesman said.
It was unclear who was in control of the base in Kitona, but President Kabila has vowed to crush the uprising and called on his supporters for help.
"Be assured we will take weapons to swiftly end this rebellion," Cabinet minister Pierre Victor Mpoyo said on state radio, quoting Mr Kabila.
The vice governor of South Kivu province, Benjamin Serukiza, said the Tutsi rebels had taken control of much of the province, including Bukavu and its airport.
"At the moment a large portion of the province is under the control of the army which is hostile to Kabila's regime," Mr Serukiza said.
Kivu region is divided into three provinces, including North Kivu, South Kivu and Maniema.
In the city of Goma, gunmen hijacked a private airplane and ordered the pilot to fly to the military base in Kitona near the Atlantic coastline on the opposite side of the country, said Mr Kabila's spokesman Yerodia Abdoulaye Ndombasi. The hijacking was led by Banyamulenge ethnic fighters.
The Congolese airplane owned by the private airline CAL touched down in Kitona about 140 miles southwest of Kinshasa, said Mr Ndombasi.
Mr Kabila convened an emergency cabinet meeting yesterday to discuss the government's response to the rebellion in the east and to earlier gun battles in two military barracks in the capital.
"The government asks Congo's neighbours not to make the wrong decisions to fight," Mr Mpoyo said in a radio broadcast following the meeting. The comment was aimed directly at neighbouring Rwanda, which Mr Kabila believes is behind the movement against his leadership. Rwandan fighters and Banyamulenge Tutsis played a key role in helping Mr Kabila march to victory last year over longtime dictator Mobutu Sese Seko. Those same fighters today, however, appear to be moving to get rid of Mr Kabila.
A delicate ethnic and military alliance that helped thrust Mr Kabila - a one-time obscure Marxist rebel - into power 14 months ago is now unraveling.
Rwandan chief of staff General Kayumba Nyamwasa denied Rwanda was involved in the mutiny, but warned that the rebellion included some of the best soldiers in Mr Kabila's army.
Congo's Justice Minister Mwenze Kongolo said the government was preparing an armed response to the rebellion in Kivu region. The ethnic Tutsi population in the area has close links with Rwanda, while Mr Kabila's support and control of the region has faltered for months.
In the capital loyal troops continued to patrol city streets and man roadblocks. A dusk-to-dawn curfew was still in effect, but life in the city began to return to normal as abandoned streets began to fill again.Reuse content