George Floyd's brother on Wednesday begged the UN to help African Americans because "black lives do not matter" in the US".
And the UN's human rights chief, Michelle Bachelet, urged reparations for centuries of discrimination.
Philonise Floyd, whose brother was killed in police custody, made an impassioned speech by video link to an urgent UN Human Rights Council debate on "systemic racism" in the US and beyond.
Ms Bachelet, the UN High Commissioner for Human Rights, said the "gratuitous brutality" of Floyd's death was an example of racism that harmed millions of people of African descent.
She urged countries to confront the legacy of slavery and colonialism, and to make reparations.
The council, in Geneva, is debating a draft resolution pushing for Ms Bachelet to investigate racism and police civil liberties breaches against people of African descent in the US.
US President Donald Trump withdrew America from the council two years ago.
Floyd, 46, died in Minneapolis on May 25 after a white police officer, who has since been charged with murder, knelt on his neck for nearly nine minutes.
Video of the incident sparked demonstrations in the US and around the world, and calls to address systemic racism.
Mr Floyd told the UN that his brother had been "tortured to death" as witnesses begged the officer to stop, "showing us black people the same lesson, yet again: black lives do not matter in the United States of America".
"You in the United Nations are your brothers' and sisters' keepers in America, and you have the power to help us get justice for my brother, George Floyd.
"I am asking you to help him. I am asking you to help me. I am asking you to help us black people in America."
Mr Floyd urged the council to establish an independent international commission of inquiry – one of the UN's highest-level investigations, generally reserved for crises such as the Syrian conflict.
An initial text presented on Tuesday on behalf of 54 African countries also proposed such an inquiry.
But the proposal was dropped and the resolution heavily watered down after opposition from Washington and some of its allies.
It now calls on Ms Bachelet to "establish the facts and circumstances relating to the systemic racism, alleged violations of international human rights law and abuses against Africans and people of African descent" by law enforcement in the US and beyond – especially those incidents that resulted in deaths.
The aim was "to ensure the accountability of perpetrators and redress for victims".
Ms Bachelet told the council that Floyd's death had brought to a head the sense of outrage felt by overlooked people and that the protests were "the culmination of many generations of pain".
"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," the former Chilean president said.
Ms Bachelet stressed the need to "make amends for centuries of violence and discrimination, including through formal apologies, truth-telling processes and reparations in various forms."
On Tuesday, Mr Trump issued an order to improve policing, calling for a ban on choke holds, unless an officer's life were at risk.
The executive order encourages training in easing tension, better recruitment, sharing of data on officers who have bad records, and money to support police in complicated duties related to people with mental or drug issues.
But it stopped well short of demands made at nationwide protests.
Andrew Bremberg, the US ambassador to the UN in Geneva, said his country was open in its commitment to addressing racial discrimination and injustice, giving Mr Trump's order as an example.
"We call upon all governments to demonstrate the same level of transparency and accountability," Mr Bremberg said.
"Sadly, there are too many places in the world where governments commit grave violations of human rights and practise systematic racial discrimination, while many of those assembled in Geneva are silent."
It remains to be seen whether the current draft resolution will pass.
The UN Human Rights Council's 47 members are due to vote on the resolution after the urgent debate, which was set to conclude on Thursday.
Wednesday marks only the fifth time in the council's 14-year history that it has agreed to hold an "urgent debate", which is like a special session but within a regular meeting of the council.
