One person has been shot dead and at least 10 injured after Kenyan police fired live bullets at demonstrators in the western city of Kisumu.
There were clashes in Nairobi at the weekend
A BBC reporter in Kisumu says police started shooting after hundreds of protesters started burning tyres.
They were protesting at President Mwai Kibaki's announcement last week that a new constitution would be delayed.
The issue has deeply divided the ruling coalition and there were street battles on Saturday in the capital, Nairobi.
Loss of faith
"The [dead] person was shot by a lady police officer after a group of demonstrators started throwing stones towards a police Landrover," provincial police chief Omar Bakari Jambeni told AFP news agency.
He also said that more than 100 people had been arrested.
"They were shouting that they want a new constitution at the same time throwing stones using slings. It forced us to use tear gas canisters and batons," he said.
The BBC's Ishbel Matheson in Nairobi says the tensions which have dogged President Kibaki's government since it came to power have now boiled over.
The public's faith in the administration has been seriously undermined, she says.
After coming to power in December 2002, President Kibaki promised to introduce a new constitution within 100 days, but the deadline was put back to 30 June this year, before being again postponed.
A leading member of the ruling Narc coalition, Raila Odinga, had been promised the new powerful post of prime minister in return for backing Mr Kibaki in the election.
A constitution review body earlier this year recommended the creation of a prime minister and the reduction of the president's powers despite opposition from Mr Kibaki's allies.
Mr Kibaki said political divisions along ethnic lines had hampered progress with the constitutional review, but that he remained committed to having a new constitution.
To shore up his authority, Mr Kibaki last week brought members of the former ruling Kanu party into government and demoted members of Mr Odinga's Liberal Democratic Party.