Nairobi: The United Nations investigator into extra-judicial killings on Wednesday said that Kenya's police chief and attorney-general should be fired because of hundreds of alleged murders by security forces.

"Kenyan police are a law unto themselves and they kill often and with impunity," Philip Alston, UN rapporteur on extrajudicial, summary and arbitrary executions, said at the end of a 10-day visit to Kenya.

The Australian official backed accusations that security forces have killed 500 suspected members of the outlawed Mungiki crime gang, 400 political demonstrators during a post-election crisis last year, and 200 suspected rebels from the remote western region of Mount Elgon.

The police and military deny all the allegations.

Alston's report, laced with sarcastic references to the authorities' failure to respond properly to the accusations, was one of the strongest indictments of impunity in Kenya.

"There is zero internal accountability - the police who kill are the very same police who investigate police killings," Alston told a news conference, saying only the rare few caught committing abuses on camera were ever prosecuted.

He accused police commissioner Hussain Ali of "stonewalling" his inquiries and responding to questions such as "how many policemen are there in Kenya?" with the phrase "not immediately available".

"Any serious commitment to ending the impunity that currently reigns in relation to the widespread and systematic killings by the police should begin with the immediate dismissal of the police commissioner," Alson said.