Dressed in a blue blazer and polo shirt, the president smiled and shook hands with reporters at the presidency in Bujumbura's city centre, and gave only a brief statement without even mentioning this week's attempt to overthrow him.
Nkurunziza has been facing weeks of violent and deadly street protests over his controversial bid to stand for a third consecutive term in office. On Wednesday a group of top generals announced they were overthrowing him while he was on a visit to neighbouring Tanzania.
Nkurunziza pointedly ignored the coup attempt and spoke only about reported threats from Somalia's Al-Qaeda-linked Shebab militants, who have warned of mounting attacks against Burundi and other states that contribute troops to the African Union force in Somalia.
"We have taken measures against Al-Shebab. We take this threat seriously," the president said.
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Addressing the domestic crisis, Willy Nyamitwe, a close aide to the president, said Burundi's election commission "could decide to delay" Burundi's parliamentary and presidential votes - although he gave no indication that Nkurunziza had changed his mind about standing for re-election.
Parliamentary elections are due to take place on May 26, and presidential polls on June 26. Nyamitwe suggested they could be delayed by "two or three days, by a week".