Burundian President Pierre Nkurunziza's spokesman said he had returned to the capital on Friday after a failed coup but that the general behind it had not been arrested as he had reported earlier, adding to confusion after three days of turmoil.

In an address on the small east African country's state radio, Nkurunziza urged an end to weeks of demonstrations over his quest for a third term in office.

"There is peace in the whole country, including in the capital city where the coup-makers were operating," he said after a day of clashes in which at least a dozen people were killed.

"Whoever wants to bring trouble in the country will not go far."

Nkurunziza's spokesman said earlier that Burundian forces had arrested Gen. Godefroid Niyombare, who had announced the president's ouster on Wednesday while he was abroad.

Niyombare "has not been arrested", presidential spokesman Gervais Abayeho told Reuters later. He said the source of his earlier statement had corrected the information.

Burundi was plunged into deep crisis after Nkurunziza announced he was running for another five-year term, with clashes between police and protesters stirring memories of an ethnically driven civil war that ended just a decade ago.

Opponents say his decision violates the constitution and a deal to end the war that pitted rebel groups of the majority Hutu population, including one led by Nkurunziza, against the army which was then commanded by minority Tutsis.

The army is now mixed and has absorbed rival factions, but the coup attempt exposed alarming divisions.

Calls for more anti-Nkurunziza rallies

Troops loyal to Nkurunziza had largely calmed the streets on Friday after frequent gunfire on Thursday.

But activists called for more rallies against the president, while some Bujumbura residents said police told them they would be fired upon at if they did demonstrate.

"Protests to reject the third term bid for Nkurunziza will continue," said Gordien Niyungeko, deputy head of Focode, one of the 300 civil society groups that backed protests. "Our movement had nothing to do with the attempted coup."

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The wife of a man killed by police, according to protesters, cries on a street in Bujumbura, Burundi, on Friday. (Goran Tomasevic/Reuters)

Until the coup attempt, protests had occurred almost daily. Protesters hurled rocks while police fired tear gas, water cannon and were even seen firing guns at the protesters.

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

More than 105,000 people have already fled to neighbouring states, including next door Rwanda, with the same ethnic mix as Burundi and which was torn apart by a genocide in 1994 that killed 800,000 mostly Tutsis and moderate Hutus.

Hundreds of people lined the streets carrying flags for the president's return to the capital from his rural home.

His spokesman said he was back in the presidential palace on Friday after returning to Burundi on Thursday from Tanzania where he had been when the coup was declared. Witnesses said they could not tell whether his motorcade had passed by.

A man with a gaping head wound lay dead in a street in Butarere, a Bujumbura district that has been a hotbed for protests. Residents said police had shot him and wounded two others. There was no immediate police comment.

A group of men in Bujumbura's Cibitoke suburb said they had been told by police that they would be treated as rebels and shot at if they demonstrated. "Now we are no longer looking for protesters, we are looking for rebels," police told them.

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Boys walk behind patrolling soldiers in Bujumbura. Activists are calling for more protests against the president, despite his call for calm. (Goran Tomasevic/Reuters)

Even before the coup attempt, officials had called protests an "insurrection".

Fighting on Thursday was at times fierce, particularly around the state radio station, a strategic asset for loyalist and supporters of the coup. An army chief said 12 rebels were killed in those clashes.

The constitution and a peace deal that ended the civil war both specify a two-term presidential limit. But Nkurunziza is seeking a third term anyway, relying on a court ruling that his first term does not count because he was appointed by parliament, not elected. His opponents and some donors have questioned the court's impartiality.

The heavy-handed response of the police to demonstrations in recent weeks has drawn stern rebukes from Western donors, who have urged the president not to run again. The United States, which provides training and equipment to the Burundian army, demanded a halt to "violent force" by police.

"...The president's decision to announce his candidacy for a third term has and will continue to exacerbate instability, and potentially foment violence in the country," U.S. State Department spokesman Jeff Rathke said in Washington on Friday.

"Any of those who ... plan or participate in or order widespread or systematic discriminatory violence against the civilian population should know that the world is watching, and that they should be held accountable," he told reporters.

The U.S. Embassy in Bujumbura was closed on Friday, non-essential staff were leaving and a decision on when to reopen had yet to be made, an embassy spokeswoman said.

Several African leaders had criticised Nkurunziza's bid for re-election in the June 26 presidential vote. The African Union also condemned any attempt to seize "power through violence".

The European Union, Belgium and the Netherlands have all suspended some aid due to the unrest, particularly donations linked to the elections, which alongside the presidential polls also include a parliamentary race scheduled for May 26.

In his radio address, Nkurunziza called on the international community to support Burundi, saying any suspension of aid by donors would only "opens doors to trouble" and help those who want to "seize power by force" rather than through democratic means.