"We have decided to surrender," coup leader General Godefroid Niyombare told the AFP news agency by phone on Friday. "I hope they won't kill us."
Loyalist troops arrested the coup leaders' spokesperson, Zenon Ndabaneze, deputy coup leader Cyrille Ndayirukiye and another senior mutineer but promised "no foul play" because they wished to put the men on trial.
Nkurunziza, who was at a regional conference in Tanzania when the coup took place, had returned to Burundi on Friday and was preparing a broadcast to show he was still in power, his aides said.
"Out of principle we are against coups, but we saw that the Burundian people were broadly welcoming of the coup attempt, which show that Burundi needs change," anti-Nkurunziza activist Vital Nshimirimana told AFP.
More than 25 people have been killed and many more wounded since the ruling CNDD-FDD nominated Nkurunziza as its candidate in 26 June polls.
The UN Security Council, the US and many other countries condemned the coup, despite criticism of Nkurunziza's bid to be reelected.
Niyombare was sacked from an intelligence post in February after criticising the president's decision.