Anti-government protesters set tyres ablaze in Kenya's capital Nairobi and the western city of Kisumu on Thursday in a third round of demonstrations organised by opponents of President William Ruto.

In Mathare, a low-income settlement in Nairobi, protesters used improvised catapults to launch stones at police in riot gear, footage on Kenyan television showed.

The police were out in force after the last protest led by opposition leader Raila Odinga on Monday descended into apparent tit-for-tat attacks by both sides.

On Monday night, a church and a mosque were set ablaze in Nairobi's low-income Kibera district and properties belonging to Odinga's family and former president Uhuru Kenyatta, who supported Odinga in the election, were vandalised.

Religious leaders and human rights groups called for calm in the aftermath, warning against the kind of ethnic fighting that killed more than 1,000 people following the disputed 2007 election.

A senior official at the interior ministry, Kithure Kindiki, echoed those concerns in a statement on Wednesday, referring to "ethnically-laced arson" in Kibera, a multi-ethnic district that saw some of the worst violence in 2007.

He vowed that no more violent protests would be tolerated. "We must halt the descent," he said.

Local television stations on Thursday showed tires ablaze in Kibera and in Kisumu, near Odinga's ancestral home. In Kisumu, crowds shouted "Baba", a nickname for Odinga, as they marched.

It was not immediately clear how the police were responding to the protesters. During the previous two protests, they have fired tear gas and water cannon.

The government says two civilians have been killed and more than 130 people, including 51 police officers, injured in protests since last week.

Odinga, who has run for president five times, says the demonstrations are over the high cost of living in the country and alleged rigging in last year's election.

Odinga challenged Ruto's victory, but the Supreme Court upheld the result in a unanimous decision.