Etienne Tshisekedi's statement posted online today adds to tensions in the vast central African nation over an election that has been indefinitely delayed.
Military and police have deployed across Congo's capital.
A court has said Kabila can remain in power until a new election. The ruling party says there is "no possibility" of one in 2017.
The opposition wants it as soon as possible. Tshisekedi is calling on people inside and outside Congo to no longer recognise Kabila's authority and calls his actions "treason."