Around a thousand people heeded the call to take to the streets of the capital, Bujumbura, with other gatherings held elsewhere in the restive central African nation.
The demonstrations peaked days of protests against the UN Human Rights Council which, on Monday, is due to hear from a government delegation which is expected to reject the report, Presstv Reported.
On Tuesday, Burundi's parliament condemned the report, saying it aimed at undermining the government and creating "chaos".
The following day, the government declared as personae non gratae three UN rights investigators, with Foreign Minister Ezechiel Nibigira saying their report was "defamatory and deceitful".
Burundi has been widely criticized for alleged rights abuses committed since 2015, but has been incensed by this latest report which points the finger squarely at Nkurunziza.
The country plunged into crisis in 2015 after Nkurunziza sought a fiercely contested third term in office that his opponents said was unconstitutional.
Turmoil since then has killed at least 1,200 people, and has forced 400,000 to flee their homes, triggering an investigation by the International Criminal Court, which Burundi last year became the first nation to leave.
The UN report accused Nkurunziza of engaging in hate speech, triggering suspected crimes against humanity.
Speaking in parliament, Interior Minister Pascal Barandagiye said the UN investigators must ask God's forgiveness for questioning Nkurunziza "otherwise they will be punished without delay".
The majority of the alleged violations were committed by members of the national intelligence service, police and military, as well as the Imbonerakure, the ruling party's youth wing, described as a militia by the UN.
Burundi on Friday threatened to quit the UN rights body accusing it of "politicization".