Over 80 people are being treated for serious injuries, according to local human rights organizations. Among the injured are three police officers.
In Matuu, about ten miles from Nairobi, around ten people were hit by bullets. At least two of them were killed.
According to the newspaper The Nation, it was the police who opened fire.
In Nairobi, the police shot tear gas and rubber bullets at demonstrators.
The demonstrations are taking place on the anniversary of widespread protests against mismanagement and harsh economic conditions when around 60 people were killed.