At least four people died and more than two dozens injured as opposition protests sparked violence during Kenya's presidential re-run, according to police and hospital sources.

Two of the victims died after police and anti-election protesters, allied to the National Supper Alliance (Nasa), clashed in its western strongholds of Kisumu and Homa Bay counties on Thursday.

The third, an unidentified man, was killed when a mob attacked him in the wee hours of Thursday morning at an estate in Kisumu.

A 19-year-old man was shot in Kisumu and died while undergoing treatment at the main hospital in the county.

In Homa Bay, a 14-year-old pupil was shot dead as he watched running battles between police and protesters.

"He was seated at the door when a bullet hit him. He fell immediately on the ground," said a neighbour.

The demonstrators where trying to block the repeat vote which has been boycotted by Nasa leader Raila Odinga, prompting clashes with police.

In Machakos County, southeast of Nairobi, a secondary school student was shot dead after police allegedly fired live bullets at demonstrators in Athi River.

The protesters had barricaded roads in Makadara estate in Athi River, blocking access to Kenya's Export Processing Zone before police moved in to disperse them.

A police statement from assistant inspector general George Kinoti said another person had been shot dead in western Homa Bay "where a large mob attacked a small police facility... and the few police officers were constrained to use live fire to protect themselves and the armoury".

The latest casualties take the death toll since a disputed August 8 election to more than 40. Rights groups say most people were killed at the hands of police.

"With tensions running high there is a very real threat of further bloodshed as the election re-run takes place," said Justus Nyangaya, director at Amnesty International Kenya.

"We are calling on the police to only use force as a last resort — unlawful police killings and other human rights violations must not be allowed to recur."

The election is being held after Kenya's Supreme Court overturned the August vote citing "irregularities" and mismanagement by poll officials.