Police in Kenya have clashed with demonstrators during the latest anti-government protests, and the state-funded human rights commission says 10 people have been killed.

Kenyan police opened fire on a crowd of advancing protesters in Nairobi on Monday, a Reuters reporter said, as scattered demonstrations broke out across the country to mark the 35th anniversary of pro-democracy rallies.

Kenya's security forces have blocked all major roads leading into central Nairobi, ahead of planned nationwide protests. Much of the city centre is deserted, with businesses shut and a heavy security presence on the streets. Some schools have advised students to stay at home.