Nairobi (AFP) - The United States on Sunday ordered non-emergency US government personnel and dependents to leave violence-torn Burundi and warned other Americans to get out "as soon as it is feasible to do so".

The State Department warning followed some of the worst violence in months of political unrest in the capital Bujumbura on Friday that left nearly 90 people dead.

"The US Department of State warns US citizens against all travel to Burundi and recommends that US citizens currently in Burundi depart as soon as it is feasible to do so," it said in a statement.

The Burundi army said 87 people were killed -- with the breakdown given by Colonel Gaspard Baratuza as 79 "enemies" and eight soldiers -- during and after coordinated assaults on three military installations early on Friday morning.

Several witnesses accused the security forces of extrajudicial killings in the hours following the attacks and overnight into Saturday morning, describing officers breaking down doors in search of young men and shooting them at close range.

Some of the victims had their arms tied behind their backs, they said.

The government was quick to clear bodies from the streets, burying them in mass graves, with critics saying the move aimed to prevent further investigation of the deaths and to disguise the real number of people killed.

Friday's fighting was the worst outbreak since a failed May coup sparked by President Pierre Nkurunziza's bid for a third term in office, which he later won in disputed elections in July.

US rights group Human Rights Watch (HRW) called Sunday for a "serious and independent" enquiry to be carried out urgently into the latest violence.

"This is by far the most serious incident, with the highest number of victims, since the start of the crisis in April," Carina Tertsakian, HRW's researcher for Burundi, said in a statement.

"A serious, independent investigation is urgently needed to find out the exact circumstances in which these people were killed," she said.

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The European Union likewise called for the perpetrators behind the violence to be brought to justice and urged Burundi's opposing sides to begin a political dialogue with Uganda acting as mediator.

The bloc stood ready to provide a financial contribution to get the talks off to an "immediate start", EU foreign policy chief Federica Mogherini and European Commissioner for Development Neven Mimica said in a joint statement.

Belgium also expressed its concern over Burundi's deteriorating security situation, with Foreign Minister Didier Reynders saying he would raise the issue at Monday's meeting of EU counterparts in Brussels.

- Echoes of civil war -

Months of street protests against Nkurunziza have devolved into frequent armed attacks, with gunfire regularly erupting at night in Bujumbura and dead bodies a frequent sight on the city's streets.

Attacks targeting the security forces have escalated, with rebels armed with assault rifles, rocket-propelled grenades and mortars attacking police convoys and targeting government installations.

Residents of Bujumbura have become used to the unrest, and despite the scale and severity of the most recent violence the city was calm on Sunday with life returning to normal.

The UN Security Council met Friday following a request from France, with UN chief Ban Ki-moon saying the attacks risked triggering "a further destabilisation of the situation" and urging all sides to hold back, according to his spokesman.

UN figures released before Friday's violence showed at least 240 people had been killed and more than 200,000 had fled abroad since May, raising fears of a return to civil war, a decade after the end of a 1993-2006 conflict between rebels from the Hutu majority and an army dominated by minority Tutsis.

Some 300,000 people were killed in the war, which began a year before a genocide of mostly Tutsis in neighbouring Rwanda.

The Security Council has said that sending UN peacekeepers to the nation remained an option, and stressed the need for urgent political dialogue.