At least two demonstrators were killed in police firing on Monday, as opposition supporters in Kenya blocked key roads and set fire to tyres in a "Day of Rage" protests aimed at overhauling the country's election commission.

The Coalition for Reforms and Democracy (CORD) alliance, which alleges that the electoral body is biased towards the president, has been staging weekly protests every Monday.

Protests took place in several towns but in Kisumu, an opposition stronghold in western Kenya, police opened fire before using tear gas and water cannon to quell the protests.

Watch: Kenya - Democracy on trial?

Word of the shootings fuelled heavy clashes in the centre of Kisumu and the working class district of Kondele. There were widespread scenes of looting and two supermarkets were destroyed.

A bullet wound was visible on one corpse, laid outside a hospital morgue by protesters who said he was hit by police fire.

Six protesters were taken to Kisumu's main hospital suffering from gunshot wounds, the Red Cross said.

Opposition leader and former Prime Minister Raila Odinga led peaceful demonstrations in the capital, Nairobi.

At least three people died in similar protests in western Kenya on May 23, two of them when anti-riot police opened fire in Siaya, while a third fatality, according to police, resulted from a fall while fleeing from tear gas in Kisumu.

The protesters, many of them supporters of Odinga, had blocked roads in Migori early on Monday, setting the scene for potential confrontation with government forces.

"This is not fair. We cannot have police shooting people every other time they are exercising their rights. This man has been shot dead while protesting," Michael Omondi, a demonstrator, told the AFP news agency.

According to images posted on Twitter, businesses and schools were also shut and transport along the busy Sirare-Kisii highway - linking Kenya with neighbouring Tanzania - had been blocked.

Many Kenyans elsewhere took to Twitter to protest against the Independent Electoral and Boundaries Commission (IEBC) with the hashtag #IEBCMustGo trending in the country.

Al Jazeera's Mohammed Adow, reporting from Nairobi, said hundreds of protesters were also amassing in the capital's Freedom Square and were planning to advance on the electoral commission building.

Kenya is to hold general elections in 15 months and the main opposition leaders have threatened to boycott them if the IEBC is not reformed.

On Friday, President Uhuru Kenyatta reiterated his call for CORD to end the protests, saying parliament's legal committee was ready to start hearing public views on how to reform the electoral authority.

"We want dialogue like yesterday but it must be held within the confines of the law. Dialogue is not about going to the streets or meeting in tea rooms," Kenyatta's office quoted him saying.

CORD wants the electoral commission scrapped. Its electronic vote results transmission system collapsed during the 2013 election that brought Kenyatta to power, beating Odinga, a result disputed by the opposition.

There are fears of a repeat of violence that erupted after the 2007 elections. About 1,200 people were killed and 600,000 forced to flee their homes.

Kenyatta and his deputy, William Ruto, were on opposing sides in 2007 but, in 2013, they united in a coalition.

They were both charged by the Geneva-based International Criminal Court with fomenting the post-election violence.

Both denied the charges, which were later dropped by the court.