Burundi police fired tear gas and beat protesters who were demanding President Pierre Nkurunziza end his bid for a third term, in a resurgence of unrest that has stoked fears of ethnic conflict in Africa's Great Lakes.

A Reuters photographer said at least eight of the flag-waving and chanting demonstrators were dragged off by police on Tuesday. Some in the crowd responded by pelting officers with stones and rocks.

Rights groups say at least 20 people have died in three weeks of clashes between security forces and protesters who say Nkurunziza's ambitions violate the constitution and a peace deal that ended an ethnically fuelled civil war in 2005.

Laying the same charges against the president, a group of renegade generals tried and failed to overthrow him last week. The government said late on Monday it would treat any future demonstrators as accomplices in the failed putsch.

But crowds gathered again in the capital's suburb of Nyakabiga on Tuesday, shouting: "We will not stop until he gives up the third term."

Diplomats say the longer unrest continues the more chance that a conflict, which up until now has been largely a struggle for power, reopens old wounds in a region with a history of ethnic killing.

South Africa said earlier on Tuesday next month's election should be postponed indefinitely until political stability had returned, as regional leaders scrambled to contain the impasse and a potential humanitarian crisis.