Mr Nkurunziza called for an immediate end to protests against his bid for a third term so that elections could be held peacefully.
At least 12 people have died in protests since Mr Nkurunziza's 25 April decision to seek re-election.
It is seen as the worst unrest to hit Burundi since a 12-year-civil war ended in 2005.
Mr Nkuruziza has rejected pressure from the US to step down.
On Wednesday, an opposition presidential candidate, Audifax Ndabitoreye, was arrested on suspicion of fuelling an insurrection. He was later released.
"I am free but they [police] might ask me to come back to hear me. I am home, my wife is crying but they are tears of joy," Mr Ndabitoreye is quoted by the Associated Press news agency as saying.
In a televised address, Mr Nkurunziza said that all those arrested would be released if the protests stopped.
Foreign ministers from four East African states are currently in Burundi in at attempt to end the crisis.
Burundi's constitutional court ruled on Monday that Mr Nkurunziza can run for a third term.
The ruling came after the court's vice-president, Sylvere Nimpagaritse, had fled Burundi, saying the court had been under pressure to endorse Mr Nkurunziza's re-election bid.
The president's spokesman Gervais Abayeho denied that judges had been threatened or pressured.
Under the constitution, presidents can only be elected to two terms in office but it was argued that his first term does not count as he was appointed by parliament.
The UN refugee agency says that more than 20,000 people have left for neighbouring countries because they fear violence could escalate in Burundi.
Mr Nkurunziza, a former rebel leader, has been in power since 2005, when he was appointed by parliament following a peace deal that ended a 12-year civil war.
He then won the 2010 presidential election after the main opposition parties boycotted the vote over concerns that it would be rigged.