Ban Ki-moon, the UN secretary-general, has dispatched an envoy to Burundi following deadly protests over the president's election bid that have raised fears of a return to war.
Ban condemned violence that has left at least six dead in two days and said those responsible should be held accountable, a statement from his spokesman said on Tuesday.
Said Djinnit - the UN envoy for the Great Lakes region, which consists of Burundi, DR Congo, Rwanda and Uganda - is to hold talks with President Pierre Nkurunziza, who on Saturday announced that he would run again for office as his party's candidate.
Protesters were back on the streets of Bujumbura, the capital, on Tuesday for a third day of anti-Nkurunziza demonstrations and the police chief appealed for people not to turn "protests into a rebellion".
Ban's comments came as security forces released leading human rights activist Pierre-Claver Mbonimpa, who was arrested during protests against Nkurunziza, his lawyer Armel Niyongere said.
"Pierre-Claver was just released by the intelligence services this afternoon," Niyongere told the AFP news agency.
The opposition argues Nkurunziza's decision to run is unconstitutional and has warned it will plunge the central African nation back into violence.
Nkurunziza, 51, has been in power since 2005, when a 12-year civil war ended.
His spokesman said on Tuesday that Nkurunziza would not back down in his bid for a third term in power.
"We won't back down, that is out of the question," presidential communications chief Willy Nyamitwe told AFP, blaming demonstrators for the violence and accusing some of them of carrying guns.
Burundi's constitution only allows a president to be elected twice, for a total of 10 years in power, but Nkurunziza argues he has only been directly elected by the people once.
Ban appealed "to Burundians to safeguard the hard won gains made in consolidating peace and democracy and urges them to resolve their differences through dialogue," the statement said.
He called on security services to remain impartial and exercise restraint in their response to demonstrations after police fired live rounds, tear gas and water cannons on protesters.
Security Council envoys, who visited Burundi in March, are due to discuss the crisis this week.