Kenyan riot police were out on the streets on Tuesday as the opposition defied a police ban and staged new demonstrations over the cost of living crisis and last year's election results.

Previous protests called by veteran opposition leader Raila Odinga have turned violent, with at least three people killed as police fired tear gas and gangs went on the rampage, attacking people and property.

The capital Nairobi was largely peaceful on Tuesday, although a bus was torched on one of the city's main roads, while youths blocked roads in several slum areas, witnesses said.

Protesters also set fires and used rocks to block roads in and out of Odinga's lakeside stronghold of Kisumu in western Kenya, they said.

Nairobi regional police commander Adamson Bungei had announced Sunday that Odinga's Azimio la Umoja coalition had been denied permission to hold the demonstrations, saying the previous protests in March were "marred with violence".

But the coalition insisted the action would go ahead.

"Police cannot decide in advance that there shall be violence and then proceed to ban political activities that are protected by the constitution. That is the making of dictatorship," it said in a statement Monday.

Odinga's side had in April announced a halt to the demonstrations to allow bipartisan talks to take place, but the process appears to have stalled.

Azimio said it would deliver a petition to President William Ruto's office on Tuesday over the "unacceptably high" cost of food, fuel and electricity.

It also planned to submit a petition to the Independent Election and Boundaries Commission showing that the results of the August election were "doctored".

Odinga narrowly lost to Ruto -- his fifth presidential election defeat -- and continues to insist that the poll was fraudulent and that victory was "stolen".

Ruto, who critics say has broken several campaign promises since taking office in September, has branded the opposition action as "nonsense".

"No property will be destroyed again. The government will stand firm to ensure and protect the life, property and business of every Kenyan," he said at the weekend.

His government has voiced concerns about the impact of the demonstrations on the economy, which is slowly recovering after the Covid-19 pandemic, but is facing high inflation and a huge debt mountain as well as a plunging currency.