Inspector General of police Joseph Boinnet says one group is now pledging allegiance to Islamic State while another one is supporting Al-Qaeda.
The one supporting ISIS is operating near Mandera while that behind Al-Qaeda is based in southern part of Kenya and within Boni Forest.
He said they are competing to spread an international jihadist agenda, which could be deadly if and when it happens.
He said the group that tried to hijack and attack a bus in El-Wak, Mandera on Monday was that of ISIS.
The attack aborted after a group of Muslims in the bus shielded Christians by refusing to be split and offering them hijabs and headscarves.
Boinnet said the Mandera gang is led by Isaak Osman Ali alias Okola, Abdifata Basre and Mohamed Bilal while the Al-Qaeda gang is headed by Omar Ahmed Abdumanan.