She made this call at the UN Human Rights Council in Geneva on June 17, reports france24.com.
Bachelet pointed to the ‘gratuitous brutality’ on display in the killing of George Floyd, a 46-year-old black man who died in Minneapolis in the US on May 25 after a white police officer -- since charged with murder -- kneeled on his neck for nearly nine minutes.
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In the meeting, council members addressed racism globally and focused on the recent calls for reform changes, particularly in the United States.
Bachelet also said that “This symbol of 'systemic racism... has become emblematic of the excessive use of disproportionate force by law enforcement, against people of African descent, against people of colour, and against indigenous peoples and racial and ethnic minorities in many countries across the globe."
"Behind today's racial violence, systemic racism and discriminatory policing lies the failure to acknowledge and confront the legacy of the slave trade and colonialism," she added.
She emphasized the need to "make amends for centuries of violence and discrimination, including through formal apologies, truth-telling processes, and reparations in various forms."
The urgent council debate on June 17 was called in response to Floyd's killing, which was caught on amateur video, sparking worldwide demands to address systemic racism in the United States and around the world.
African countries have been calling for the council to ask Bachelet and other UN rights experts to investigate racism and policy brutality in the US, but potential support for their draft resolution is unclear.
However, the US withdrew itself from the council two years ago, while a number of its allies are uncomfortable with the country being singled out in the text, according to observers of the process.
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Bachelet herself did not speak out specifically in favour of the draft resolution, but she did stress the need for "decisive reforms".
She insisted on the importance of making clear that "black lives matter. Indigenous lives matter. The lives of people of colour matter."
"All human beings are born equal in dignity and rights: that is what this Council, like my office, stands for."