Rights group suspects state complicity in execution-style deaths of up to 450 men.
In the capital Nairobi’s volatile Westlands constituency, gunshots were fired into the air to scare rival supporters, vehicles smashed and an election official briefly kidnapped.
“The situation is very tense,” the official said after he was released.
In western Kenya, police fired tear gas to disperse demonstrators disputing the way some candidates had been nominated.
Officers arrested one man who was wielding a machete.
Elsewhere, armed members of tribal groups demanding an end to a land distribution scheme in the Mount Elgon region, near the border with Uganda area, opened fire on a vehicle that was carrying ballot boxes.
Witnesses said an election official and four policemen were injured.
A man was shot on the head at another polling station in the western region, police officials said.
Police said several people had been arrested as security forces moved to clamp down on the unrest that has become a feature of the pre-election period.
“There has been confusion all over between supporters of rival candidates, but we have not received any reports of fatalities,” Eric Kiraithe, a police spokesman, said.
Local television stations also reported delays, cancellations, boycotts, demonstrations, missing or stolen polling papers and brawls in many of the country’s 210 constituencies.
About 14 million Kenyans are eligible to cast ballots in the polls to be monitored by the European Commission, the African Union, the Commonwealth and local civil groups.