Veteran opposition leader, Etienne Tshisekedi, said he did not recognise the government of the Democratic Republic of Congo (until last week, Zaire) which excluded him.
"This government doesn't exist for me. I ask all the people to resist with their last energy all attempts to impose a government without popular legitimacy," Mr Tshisekedi said.
He called for the withdrawal of foreign troops who helped Mr Kabila's guerrilla alliance drive veteran dictator Mobutu Sese Seko from power in the former Zaire.
Hundreds of Tshisekedi followers chanted anti-Kabila slogans and called for the pull-out of Rwandan troops from his Alliance.
They marched from Mr Tshisekedi's house in Limete into the city centre, past the US, French and Belgian embassies, but troops firing in the air blocked them before they reached the People's Palace, the seat of parliament.
At his news conference, Mr Tshisekedi did not directly ask his fanatical supporters in the the city of five million people to take to the streets. He appear-ed to leave the door open for talks with Kabila, acknowledging that the guerrilla leader deserved to be president but insisted on "popular legitimacy".
Mobutu, who went into exile on Sunday, arrived in Morocco from the West African state of Togo, on Togo president Gnassingbe Eyadema's official plane.
Sources close to Eyadema said Mobutu would go on to France, where he has a Riviera villa, after the French elections, which end on 1 June.
Weakened by cancer, Mr Mobutu left Congo with his wife and children, including his son Captain Mobutu Kongolo, and an entourage of about 50 people on Eyadema's presidential Boeing. A DC-8 was expected in Lome later to collect his extensive luggage.
Giving the new government a more sympathetic reception, South African Deputy President Thabo Mbeki said he would not try to persuade Kabila to include Tshisekedi and warned against pressure for quick elections, saying there were serious obstacles to achieving a fair poll so soon after taking power.
Across the river from Kinshasa, neighbour Congo noted the change of power in former Zaire and said it was ready to support efforts of the new authorities to promote democracy. In a tacit acknowledgement of Mr Kabila's decision to rename Zaire as the Democratic Republic of Congo, its neigh- bour referred to itself as Congo Brazzaville - the name it used before 1971 when the two nations had the name Congo in common.