"The premier tendered his resignation to the president at 1:00 pm" (1200 GMT), a source in the prime minister's office told AFP. "The president took note of it and told him to handle all current business."
A cabinet spokesman confirmed Badibanga's resignation.
Kabila had announced in a speech Wednesday that he would name a new prime minister "within 48 hours" and urged the opposition "to overcome its internal squabbles" and hand him a list of candidates for the post of prime minister.
The agreement would allow Kabila, 45, to remain in office until elections in late 2017, ruling in tandem with a transitional watchdog and a new premier, to be chosen from within the opposition ranks.
The transitional watchdog was to have been headed by veteran opposition leader Etienne Tshisekedi, who had gathered together an opposition coalition called "Rassemblement" (Unity), but died in early February.
The country, which suffered through two wars between 1996 and 2003, has not had a democratic transition of power since its independence from Belgium in 1960.
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