Local media reported at least one killed in Kisumu in the west of the country, while police in Nairobi and the second city of Mombasa fought running battles with small groups of protesters.
The opposition CORD party claimed several people killed, but there was no immediate police confirmation of any casualties.
“Innocent Kenyans have lost lives today,” opposition CORD party leader Raila Odinga told reporters. “We must condemn this in the strongest terms possible.”
The opposition claimed in a statement that its supporters were “killed in various parts of the country,” without giving a number.
Police had banned the planned demonstrations and scores of officers in riot gear guarded the building that houses the election commission headquarters in the centre of the capital.
They fired tear gas cannisters and stun grenades to disperse groups of onlookers and used water cannon to douse people who did not move quickly enough along a nearby pedestrian overpass.
The clashes followed violent protests in the city centre last week and the acrid smell of tear gas filled the city’s usually traffic-clogged streets.
– ‘Civil disorder’ –
In Nairobi’s Kibera slum, police also fired tear gas as dozens of demonstrators blocked the road with burning tyres, with some hurling rocks, an AFP reporter said.
Clashes were also reported in the main port city of Mombasa, and in the small western town of Kakamega, according to the Daily Nation newspaper.
Odinga, a former prime minister who lost his bid for the presidency in 2013, accuses the election commission of bias towards President Uhuru Kenyatta and has demanded new commissioners be named ahead of elections due in August 2017.
Kenyatta beat Odinga by more than 800,000 votes to win the presidency in 2013. Odinga and civil society groups accused the electoral commission of a series of irregularities that they said skewed the results.
The election nonetheless passed off peacefully, in contrast to the country’s disputed 2007 elections which degenerated into fierce inter-ethnic violence that killed more than 1,100 people after Odinga’s supporters challenged his defeat by Mwai Kibaki.
The next election is shaping up as a rematch of 2013, with 71-year-old Odinga aiming to unseat Kenyatta, 54.
“It is the same issues of election fraud and malpractice that led to the mayhem and conflict that is also the genesis of the current conflict,” CORD added in a statement.
“It is evident that unless these are addressed now, well before any general election Kenya is going to be thrown into another cycle of civil disorder.”