Two protesters died from gunshot wounds and at least eight were injured in Matuu, Machakos County on Wednesday as demonstrators marked one year since mass anti-government protests in Kenya, a hospital official told AFP.

"One had abdominal gunshot wounds and died from excessive bleeding. We got an alert of another gunshot victim at another hospital but on arrival we found that the patient had already succumbed," said Julius Makau, administrator at a hospital in Matuu.

It was not immediately clear how the victims sustained the gunshots wounds. The Nation newspaper reported police had opened fire.

Protesters were marching to mark a year since the peak of demonstrations over the economy that saw at least 60 people killed by security forces.

In Nairobi, AFP journalists saw demonstrators engaged in running battles with police, who appeared to use primarily tear gas and rubber bullets as they sought to control the crowd.

Protests have also been reported in other towns and cities across Kenya.

Makau said his hospital had received six people with gunshot wounds and three with other injuries, leading to one death. One patient was in critical condition, while the rest were stable, he said.