Another opposition figure who lives in exile, Hussein Radjabu, urged Burundians to use other means to push Nkurunziza out of power, raising the possibility of renewed violence.
Nkurunziza had campaigned forcefully for the constitutional changes that include extending the president's term from five years to seven, making him the latest African leader to prolong his stay in office. That could give him another 14 years in power when his current term expires in 2020.
The referendum raised concerns about bloodshed in Burundi that has seen deadly political violence since April 2015, when Nkurunziza sought and ultimately won a disputed third term.
Nkurunziza's opponents say he already has ruled longer than the constitution allows.
The 54-year-old Nkurunziza, a former rebel leader, rose to power in 2005 following a peace deal ending a civil war in which some 300,000 people died. He was re-elected unopposed in 2010 after the opposition boycotted the vote.
Nkurunziza in 2015 asserted he was eligible for a third term because lawmakers, not the general population, had chosen him for his first term. Critics called the third term unconstitutional as the deal ending the civil war says the president can be re-elected only once, but the constitutional court said Nkurunziza could run again.
More than 1,200 people have been killed in in sporadic violence since April 2015, according to the United Nations.
International Criminal Court judges last year authorized an investigation into allegations of state-sponsored crimes - a decision unaffected by Burundi's unprecedented withdrawal from the ICC.
Observers ahead of the vote expressed alarm at reported violence and intimidation of the referendum's perceived opponents, including threats of drowning and castration.
A presidential decree criminalized calls to abstain from voting, with a penalty of up to three years in jail.
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