Burundian riot police have forcibly dispersed crowds protesting against the president seeking a third term, a decision critics said is unconstitutional and could rekindle turmoil after a decade of calm in the East African state.

Witnesses said police used water cannon and tear gas and in some cases live bullets to scatter demonstrators in four districts of Bujumbura after President Pierre Nkurunziza's government banned protests for or against his move.

At least one police officer and a protester were injured in the disturbances. Police had no immediate comment.

Burundi's ruling CNDD-FDD party nominated Mr Nkurunziza as its presidential candidate on Saturday, prompting hundreds of civil society groups to condemn the move as a "coup" against the constitution, which limits leaders to two terms in office.

Those opposed to a third term also say it goes against the spirit of a peace deal signed in 2000 that has kept Burundi calm for a decade since a civil war between ethnic Hutus and Tutsis in the small, coffee-growing nation ended in 2005.

United Nations and Rwandan officials say more than 17,000 Burundians have fled into neighbouring Rwanda and the Democratic Republic of Congo since mid-March due to rising fear of violence in the run-up to the June 26 presidential election.

"We deplore the way police acted with violence against a peaceful demonstration," Janvier Bigirimana, a civil society activist, said of Saturday's events.

Interior Minister Edouard Nduwimana said the demonstrations were illegal because the government had banned any protest for or against the president pursuing a third term.