The United Nations, the European Union and African nations urged Burundi's government and the opposition on Sunday not to let violence derail dialogue, after an opposition politician was shot dead and some groups said they were boycotting talks.

UN Secretary-General Ban Ki-moon and others condemned the killing by unidentified gunmen on Saturday of Zedi Feruzi, the head of the UPD party, who opposed President Pierre Nkurunziza's bid for a third five-year term.

Nkurunziza's decision to run again has triggered the worst crisis in the small African country since the end of an ethnically charged civil war in 2005. The longer unrest lasts, the more chance of a return to ethnic violence, diplomats say.

UN special envoy to the region, Said Djinnit, the African Union and other regional African states have been sponsoring dialogue between rival sides since May 5 to end the crisis.

"They strongly urge all participants to remain fully engaged in the dialogue," the sponsors said in a joint statement after the latest round of talks in Bujumbura on Sunday that were boycotted by some parties and civil society groups.

Separately, the EU, the biggest donor to aid-reliant Burundi, urged "all parties to engage in good faith" in talks.

READ: Belgium suspends aid for Burundi elections

Opponents say Nkurunziza's re-election bid violates a two-term limit in the constitution and a peace deal that ended civil conflict. Protesters have regularly clashed with police in the past month and unrest provoked a failed military coup on May 13.

The president, who has called protests an "insurrection", points to a constitutional court ruling that said his first term, when he was picked by parliament not a popular vote, did not count. He has shown no signs of backing down from his bid.

The UN secretary-general called on parties involved in talks "not to be deterred by those who, through violence, seek to prevent the creation of an environment conducive to peaceful, credible and inclusive elections in Burundi," his office said.

A presidential vote is scheduled for June 26, while parliamentary and local council polls are due on June 5, after a delay of just over a week in the wake of the unrest.

Following Feruzi's killing, Anshere Nikoyagize, the head of the civil society group Ligue ITEKA, told Reuters that civil society groups and opposition parties would not attend the dialogue, which began this month. But he did not name them.

"We can't negotiate with the president of the republic with regards to the violation of the constitution or the violation of the Arusha accord. It is impossible," said Frederick Bamvuginyumvira, vice president of opposition party Frodebu.

Willy Nyamitwe, presidential media adviser, told Reuters that Sunday's talks had gone ahead with some civil society groups and two parties, but also did not provide a list. Burundi has dozens of registered parties.

"The main objective is to find ways of coming out of this situation," Nyamitwe said. "This situation is going out of control."

Burundi's crisis has set the region that has a history of ethnic conflict on edge. More than 110,000 Burundians - about 1 per cent of the country's population - have already fled across the border for fear violence will spread outside the capital.

Till now, there has been little sign of progress in bridging differences between the two camps. The president has insisted he will follow his party's call to stand again, while opponents say protests will continue until he ends his bid.

The Red Cross has said the death toll based on people its workers have seen killed stands at about 20. Emergency workers say that the total number could be double that. -REUTERS