A young man was shot dead during violent clashes between Kenyan police and anti-government protesters, and police also targeted the convoy of opposition leader Raila Odinga and his supporters with tear gas, amid escalating looting in the unrest.

Odinga has called on Kenyans to demonstrate every Monday and Thursday, accusing President William Ruto of rigging the presidential election and failing to curb the rising cost of living.

The demonstrators defied police chief Japhet Komi, who a day earlier announced a ban on unlicensed demonstrations, especially in the capital Nairobi and Odinga stronghold of Kisumu, warning he would tackle any violence.

The main hospital in Kisumu, western Kenya, reported a young man shot dead in the city, the second reported death since demonstrations began on Monday, and an organisation responsible for monitoring police misconduct said in a statement it had opened an investigation into "an incident in which police shot and killed a man."

Police used tear gas canisters in Nairobi and Kisumu to disperse demonstrators, and targeted Odinga's convoy with tear gas and water cannons as it passed through a busy neighbourhood of Nairobi.

In parallel to the demonstrations, media reports said hundreds of looters attacked former President Uhuru Kenyatta's farm on the outskirts of Nairobi, stealing sheep, cutting down trees and setting fire to parts of it.

Monday's demonstrations turned violent, killing a university student and injuring 31 policemen, and authorities arrested dozens of dissidents.

The violence is the first since Ruto came to power six months ago after beating Odinga in an election he claims was "stolen" from him.