Kenyan police lobbed tear gas at opposition supporters who protested around the country on Monday to demand a reform of the election commission before new polls are held later this month.

Thousands gathered in the capital and the western opposition stronghold Kisumu, while smaller demonstrations took place elsewhere, as the opposition stepped up its protest campaign from two to three days a week.

Opposition leader Raila Odinga reiterated that he would not take part in a re-run of the presidential election on October 26 if his demands are not met.

"We have said and we continue to say that we will not participate in the elections if the environment is not conducive for a free and fair election," he told a press conference.

Kenya's Supreme Court last month overturned the August election of President Uhuru Kenyatta citing "irregularities" in the counting of results.

With just over two weeks to go until the new election, and rival sides hardening rhetoric, uncertainty is growing over whether they will be able to agree on the conduct of the poll in time.

A rights group said Monday it had documented 37 deaths in the days following August's poll, with most victims killed by police.

Odinga has called for protests on Mondays, Wednesdays and Fridays.

In western Kisumu businesses shut on Monday as large crowds of protesters gathered, before police later fired tear gas and engaged in running battles with some demonstrators.

Protests in the town of Machakos, 60 kilometres (37 miles) outside Nairobi, also turned rowdy. A small demonstration in coastal Mombasa quickly fizzled out.

In the capital itself, some 2,000 people marched through the streets before gathering in a park to hear angry speeches from opposition leaders denouncing the electoral commission.

Odinga accused Kenyatta and his deputy William Ruto of paying his supporters to defect, after another high-profile opposition member dropped out.

On Saturday former Mombasa senator Hassan Omar pledged allegiance to the Jubilee ruling party.

Opposition leaders also slammed efforts by ruling party lawmakers to change electoral laws which they say will facilitate poll rigging.

Outspoken opposition senator James Orengo said that if the laws were passed it would amount to "declaring war to the people of Kenya."