Kenya's President William Ruto has nominated Douglas Kanja to be vetted for the post of inspector general of police, Ruto's office said on Thursday, to replace the police chief who quit amid criticism of police conduct over anti-government protests.

Kanja had been acting in the same position since mid-July, when the previous holder, Japhet Koome, resigned after condemnation of officers' performance during protests the previous month in which at least 39 people had been killed.

The demonstrations against proposed tax increases began peacefully but turned violent.

Kanja is a career police officer with nearly four decades experience, having served as the deputy inspector general of Kenyan police and commandant of the police's paramilitary General Service Unit.

Rights groups and activists have since said the death toll from the protests countrywide stood at at least 50.

The mostly youth-led protests have continued even after Ruto withdrew the legislation, and fired almost all of his cabinet.

Activists say they want Ruto to resign and are calling for systemic changes to clean up corruption and address poor governance in national and regional county governments.

On Wednesday, Ruto named the remainder of his cabinet, which includes four members of the main opposition party to a "broad-based" cabinet he promised in response to the protests, but activists criticised the new government as a corrupt bargain.

On Thursday, police threw tear gas to disperse a small crowd in the centre of the capital that was preparing a march to present a petition to government offices in memory of those killed in the protests, according to Reuters witnesses.