Shots rang out in the capital Kinshasa, where at least nine people were killed, and there was sustained gunfire in the country's second-largest city, Lubumbashi, where two died -- including a policeman who was lynched by an angry crowd.
In central Kananga the sound of heavy weapons sent crowds of panicked residents pouring into the streets, but there were no reports of clashes in northeastern Kisangani or in Bukavu in the country's east.
Tension has been mounting for months in DR Congo ahead of the December 20 deadline for Kabila's second and final term in office to end.
With no election planned and no sign of him stepping down, veteran opposition leader Etienne Tshisekedi issued a plea to the country's 70 million people to "peacefully resist" and "reject" the Kabila regime.
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Plumes of smoke from burning barricades hung over Kinshasa after overnight protests, and activity ground to a halt as troop carriers patrolled the largely empty streets of the megacity of 10 million.
Local authorities said "police were forced to fire into the air to disperse civilians" because some protesters were armed. It was impossible to immediately verify that claim.
"Fortunately, we are not back to the slaughter of September," said national police spokesman Pierre-Rombaut Mwanamputu, referring to bloodshed in September when at least 53 anti-Kabila protesters died in two days, according to the UN.
Kabila, 45, who has ruled since 2001, is constitutionally barred from seeking a third term but under a controversial recent constitutional court order, he may stay on until a successor is chosen.
"There was teargas and gunfire," said Andre, a resident of Kinshasa's Matete neighbourhood, adding that security forces "threatened the population".
And in what Kabila's opponents dubbed "a provocation", state TV overnight announced a new government.
Headed by Samy Badibanga, it is part of an October deal between the ruling party and tiny fringe opposition groups that enables Kabila to remain in office pending elections in April 2018.
But the main opposition bloc rejects the plan.