An AFP correspondent in the city saw police tear-gas opposition supporters who had massed in the morning outside the offices of the Unafec party headed by Antoine-Gabriel Kyungu wa Kumwanza.
"Kabila must go", "Come kill us, we've had enough", shouted some of the protesters, who hurled stones at police.
Lubumbashi is the second biggest city of Democratic Republic of Congo, where the authorities are under pressure from the international community to hold presidential elections as planned in November when Kabila's second -- and constitutionally last -- mandate ends.
He first assumed power after his father, president Laurent Kabila, was assassinated in 2001. He took up his first elected term in 2006, under a new UN-supervised constitution which provided for two five-year mandates in the vast nation of some 81 million people.
Yesterday, Unafec's offices in the capital Kinshasa were vandalised while today in Lubumbashi, men claiming to be police tore down pictures of the former governor of Katanga, Moise Katumbi, who joined the opposition in September.