The 93-year-old Mugabe, the world's oldest head of state, has long been criticised at home for going overseas for medical treatment as Zimbabwe's once-prosperous economy falls apart. Mugabe also faces US sanctions over his government's human rights abuses.
"This appointment clearly contradicts the United Nations ideals of respect for human rights and human dignity," the State Department said.
"The decision to appoint Robert Mugabe as a WHO goodwill ambassador is deeply disappointing and wrong," said Dr. Jeremy Farrar, director of the Wellcome Trust, a major British charitable foundation. "Robert Mugabe fails in every way to represent the values WHO should stand for."
With Mugabe on hand, WHO director-general Tedros Ghebreyesus of Ethiopia announced the appointment at a conference in Uruguay this week on non-communicable diseases.
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Tedros, who became WHO's first African director-general this year, said Mugabe could use the role "to influence his peers in his region" on the issue. He described Zimbabwe as "a country that places universal health coverage and health promotion at the center of its policies." A WHO spokeswoman confirmed the comments to The Associated Press.
The groups said they had raised their concerns with Tedros on the sidelines of the conference, to no avail.
The heads of UN agencies typically choose celebrities as ambassadors to draw attention to issues of concern. The choices are not subject to approval by the UN secretary- general or anyone else.
The ambassadors hold little actual power. They also can be fired. The comic book heroine Wonder Woman was removed from her honorary UN ambassador job in December following protests that a white, skimpily dressed American prone to violence wasn't the best role model for girls.
The southern African nation once was known as the region's prosperous breadbasket. But in 2008, the charity Physicians for Human Rights released a report documenting failures in Zimbabwe's health system, saying Mugabe's policies had led to a man-made crisis.
"The government of Robert Mugabe presided over the dramatic reversal of its population's access to food, clean water, basic sanitation and health care," the group concluded. Mugabe's policies led directly to "the shuttering of hospitals and clinics, the closing of its medical school and the beatings of health workers."
The US in 2003 imposed targeted sanctions, a travel ban and an asset freeze against Mugabe and close associates, citing his government's rights abuses and evidence of electoral fraud.