President William Ruto on Tuesday said all Kenyans must obey the law a day after anti-government protests turned violent with police firing tear gas and looters going on a rampage.

The African Union appealed for calm and political dialogue after demonstrations called by opposition leader Raila Odinga rocked Nairobi and the western city of Kisumu.

The veteran opposition leader has called for regular protests every Monday and Thursday, accusing Ruto of stealing last year's election and of failing to control the surging cost of living.

Ruto, who is on a diplomatic visit to Germany, said impunity would not be tolerated and all Kenyans must submit to the rule of law.

"That is what makes us equal. Nobody should trample on the rights of others," Ruto said in a statement, adding he would ensure the right to life, property and business was protected.

"We have deliberately offered the police operational and financial independence to work. It is their duty to ensure that everyone adheres to the rule of law," he said.

On Monday, police fired tear gas in Nairobi and Kisumu -- an Odinga stronghold -- to disperse crowds, aiming canisters at cars carrying journalists in the capital.

Officers also used tear gas and water cannon as Odinga's convoy moved through a congested neighbourhood in Nairobi, sending people running for cover.

One man was shot dead in Kisumu, the head of the city's main hospital told AFP, the second fatality reported since the demonstrations kicked off the previous Monday, when a university student was killed by police fire.

The protesters had defied a warning by the Inspector General of Police Japhet Koome that the demonstrations were "illegal".

AU Commission head Moussa Faki Mahamat on Tuesday voiced "deep concern" at the violence and appealed for calm.

"The chairperson urges all stakeholders to exercise calm and engage in dialogue to address any differences that may exist in the supreme interest of national unity and reconciliation," Faki's office said in a statement. 

Faki "expresses deep concern at violence... which has resulted in loss of life, damage of property and the interruption of certain economic activities," his office added.

 'Stop this madness' 
Hundreds of looters descended on former president Uhuru Kenyatta's vast farm on the outskirts of Nairobi, stealing sheep and cutting trees before setting a section of the property on fire. 

Kenyatta backed Odinga's candidacy in the presidential poll in August last year after falling out with his former deputy Ruto.

Gangs also targeted Odinga's gas company Spectre International Ltd in Nairobi.

The violence has sparked worry among Kenyans, who are already grappling with skyrocketing inflation and a jobs crisis.

"Stop this madness," the Daily Nation newspaper headlined on Tuesday.

The National Cohesion and Integration Commission, a peace-building body set up after the 2007-2008 post-election clashes that killed more than 1,100 people, also called for dialogue "as a means of moving our country forward".

"The wanton destruction of cars, mosques, churches etc is not acceptable and is hereby condemned in the harshest terms possible," commission chairman Samuel Kobia said in a statement on Tuesday.

Koome said two police vehicles were destroyed in the chaos and 23 officers injured. 

"Our investigation into the destruction and injuries caused has began, and those found culpable shall face the law," he said in a statement. 

 Subsidies cut 
Police said they had received reports of the unrest at Kenyatta's and Odinga's properties and had "responded swiftly and prevented further crimes".

Ruto, who is on a four-day trip to Germany and Belgium, last week urged his rival to halt the demonstrations.

"I am telling Raila Odinga that if he has a problem with me, he should face me and stop terrorising the country," he said Thursday.

Many Kenyans are struggling to put food on the table, battling high prices for basic goods as well as a plunging local currency and record drought that has left millions hungry.

During the election campaign, Ruto portrayed himself as champion of the downtrodden and vowed to improve the lot of ordinary Kenyans.

But he has since removed subsidies for fuel and maize flour -- a dietary staple.

And last week, Kenya's energy regulatory body announced a hike in electricity prices from next month, despite Ruto insisting in January there would be no such increase.