Deputy Inspector General of Police Grace Kaindi has said the twin attacks Hindi and Gamba was the work of members of the Mombasa Republican Council (MRC). Kaindi said the attacks that left 21 people dead was pre-planned.
Kaindi said police had also discovered a blackboard abandoned in Lamu County which had writings that could incite communities against each other.
No one has been arrested over the killings.
GSU officers have been deployed to Tana Delta and Lamu following the Saturday night attacks.
Five of the killed people were prisoners in police cells who died when a group of about 50 people attacked Gamba police station.
During the attacks, three prisoners escaped, one policeman killed and two others sustained injuries in the gunfight. 10 other prisoners who were in a different cells were unhurt.
Seven building and a church were burnt criminals attacked Hindi area in Lamu at around 11 pm on Saturday.
Deputy President William Ruto has ordered security agencies to get the attackers who killed 21 people in Gamba and Hindi "dead or alive".
He gave top security chiefs in Nairobi and Lamu 48 hours to either arrest the criminals or quit the service.
Addressing a meeting in Mpeketoni and Hindi after visiting homes of the deceased in Saturday's incident, Ruto said: "The security team must get these criminals. "Starting from Inspector General David Kimaiyo to the police constable down here...these people must be arrested? The criminals are here in Lamu. We want the security team to show results of the operation in 48 hours." This is as clear as it should get.
He directed the security team in Lamu to provide the Government with a plan of how they were going to deal with the criminals.
Ruto said it was unacceptable for a country claiming to be independent to have people killed at will. "Those who perpetuated this mayhem must be either arrested or killed."