Locals in the northern district where the initial attack took place also said that fighting between police and gunmen had continued for a second day.
The previous police death toll from Saturday’s attack on officers pursuing cattle thieves was 11.
But a police source who did not want to be identified told AFP: “More bodies have been recovered – the total is now 29″ – including 26 police officers and three bandits.
“Of the 18 bodies found this afternoon, 15 are policemen,” added the source.
The remoteness of the northern Baragoi district, where the attack took place, explained why it took a day after the attack for the bodies to be discovered, said the source.
Witnesses to the attack told AFP that the attackers had used heavy weapons against the police officers.
“More than 20 people were killed, new bodies were taken away and the fighting continued all day (Sunday),” one resident, Paul Lenaimadu, told AFP.
“Now we fear (police) reprisals because the force that is going to be used to pursue the cattle thieves is not going to be directly only against them and a lot of innocents will suffer,” he added.
The group of rustlers police were pursuing were already suspected of killing 13 people in another raid on October 30.
They only set out after the rustlers when a deadline for the return of the cattle expired.
Another nine policemen are recovering from their injuries in hospital in Nairobi, hospital spokesman Kibet Mengich said.
Cattle theft and the ensuing clashes between rival nomadic groups claim dozens of lives every year in arid northern Kenya. It is rare however for police officers themselves to be attacked.
But police numbers there are low and the officers are poorly equipped. The cattle herders have therefore armed themselves against attacks from rival groups.
Elsewhere in Kenya, in the southeast Tana River region, inter-communal violence claimed more than a hundred lives in August and September.