In addition to urging the government to protect Nigerians' "fundamental right to peaceful assembly and protest" and demanding probes of any violence against demonstrators by the military and police, Bachelet called for also investigating reports that unidentified groups carrying cudgels, cutlasses, sticks, and guns are attacking protesters, sometimes with the support of security forces.
Human Rights Watch also corroborated reports that the Nigerian army had opened fire on protesters on Tuesday in what the NGOs described as "a shooting spree". "For you to do otherwise will amount to undermining national security and law and order".
The African Union also welcomed the Nigerian government's move to disband the highly controversial Special Anti-Robbery Squad (SARS).
This week's scenes have touched a chord with Black Lives Matter supporters in the United States, while the USA government has strongly condemned the "use of excessive force by military forces who fired on unarmed demonstrators in Lagos, causing death and injury".
On Thursday night President Buhari urged protesters to stop demonstrating and instead engage with the government "in finding solutions". Why is the call for police reform resonating so loudly among Nigerians who say they have had enough?
The city of 20 million is under a round-the-clock curfew imposed after almost two weeks of protests against police brutality - the West African nation's biggest wave of unrest since the end of military rule in 1999.
How major United States stock indexes fared Wednesday
Its rise helped lift the Australian dollar, weighed down by expectations of a rate cut in November, from Tuesday's three-week low. The Nasdaq composite extended its losing streak to a fifth day, falling 192.67 points, or 1.7%, to 11,478.88.
Looting and gunfire continued in Nigeria's second-largest city Thursday.
The Delta state police public relations officer, Onome Onowakpoyeya said that perpetrators were "hoodlums" protesting under the guise of demonstrators.
Vice President Yemi Osinbajo said his "heart goes out" to the victims of the recent violence and promised that there would be "justice for all".
The army has denied soldiers were at the site of the shooting at Lekki toll gate in Lagos, where people had gathered in defiance of the curfew.
Buhari in a national address Thursday night didn't mention the shootings that sparked global outrage, and resentment lingered with the smell of charred tires Friday in Nigeria's relatively calm streets. United Nations secretary-general António Guterres has called for an end to police brutality in Nigeria, while United Nations high commissioner for human rights Michelle Bachelet has acknowledged that "root and branch" reform of the security sector is necessary.
Nigeria, where many live in extreme poverty and where the median age is 18, is a tinderbox of economic and social grievances.
"We welcome an immediate investigation into any use of excessive force by members of the security forces", Secretary of State Mike Pompeo said in a statement.
The spreading of "deliberate falsehood and misinformation, in particular through social media" was, he said, "a ploy to mislead the unwary within and outside Nigeria into unfair judgement and disruptive behaviour".