"This virus is exposing endemic inequalities that have too long been ignored," she said in a statement.
Similar inequalities were also fuelling the widespread protests over the police killing in Minneapolis last week of Floyd, an unarmed black man.
"In the United States, protests triggered by the killing of George Floyd are highlighting not only police violence against people of colour, but also inequalities in health, education, employment and endemic racial discrimination," Bachelet said.
Floyd was killed when a white police officer knelt on his neck, and video images of his killing have sparked demonstrations in hundreds of US cities against police brutality and racism.
It has been the most widespread unrest in the United States since 1968, when cities went up in flames over the slaying of civil rights leader Martin Luther King Jr.
Bachelet meanwhile stressed that entrenched racial discrimination is taking a heavy health toll during the pandemic, which has killed more than 375,000 people out of nearly 6.3 million infected worldwide.
In the United States, which is the worst-hit country with over 105,000 deaths, she noted that the virus death rate for African Americans is reported to be more than double that of other racial groups.
Her statement also highlighted the situation in Britain, where government data for England and Wales shows a death rate for blacks, ethnic Pakistanis and Bangladeshis that is nearly double that of whites.
And she pointed to Brazil, where people of colour in Sao Paulo are 62 percent more likely to die from the virus than whites, and in France's heavily minority-inhabited Seine Saint-Denis suburb of Paris, which has reported higher excess mortality figures than other areas.
"The appalling impact of Covid-19 on racial and ethnic minorities is much discussed, but what is less clear is how much is being done to address it," Bachelet said.
"Urgent steps need to be taken by states, such as prioritising health monitoring and testing, increasing access to healthcare, and providing targeted information for these communities."
She said the disparities likely resulted from a range of factors linked to marginalisation, discrimination and access to healthcare, along with economic inequalities, overcrowded housing and environmental risks.
People from racial and ethnic minorities are also more likely to have jobs that require them to leave their home, like the transport, health and cleaning sectors, raising the risk of infection.
"It is a tragedy that it took Covid-19 to expose what should have been obvious -- that unequal access to healthcare, overcrowded housing and pervasive discrimination make our societies less stable, secure and prosperous," Bachelet said.
She stressed that such factors were likely playing a devastating role in many countries, but lamented that a vast majority of states do not disaggregate data by ethnicity, making it difficult to get to the root of the problem.
"Collection, disaggregation and analysis of data by ethnicity or race, as well as gender, are essential to identify and address inequalities and structural discrimination that contribute to poor health outcomes, including for Covid-19.
"The fight against this pandemic cannot be won if governments refuse to acknowledge the blatant inequalities that the virus is bringing to the fore," Bachelet warned.
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