In a tweet, WHO director-general Tedros Ghebreyesus said: “I'm listening. I hear your concerns. Rethinking the approach in light of WHO values. I will issue a statement as soon as possible.” Mugabe, 93, the world's oldest head of state, has long been criticized at home for going overseas for medical treatment as Zimbabwe's once-prosperous economy falls apart.
He also faces US sanctions over his government's human rights abuses.
The US called the appointment of Mugabe by WHO's first African leader disappointing.
This appointment clearly contradicts the United Nations ideals of respect for human rights and human dignity, the state department said.
Health and human rights leaders chimed in. 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.
Ireland's health minister, Simon Harris, called the appointment offensive, bizarre, while Kenneth Roth, the head of Human Rights Watch, tweeted: ''Mugabe corruption decimates Zimbabwe health care.
With Mugabe on hand, Tedros announced the appointment at a conference in Uruguay this week on non-communicable diseases.
Tedros, a former Ethiopian official who became WHO's first African director-general this year, said Mr 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 centre of its policies.
Two dozen organizations - including the World Heart Federation and Cancer Research UK - released a statement criticising the appointment, saying health officials were shocked and deeply concerned and citing his long track record of human rights violations”. The groups said they had raised their concerns with Mr Tedros on the sidelines of the conference, to no avail.
The heads of UN agencies typically choose celebrities and other prominent people as ambassadors to draw attention to global issues of concern, such as refugees (Angelina Jolie) and education (Malala Yousafzai). The choices are not subject to approval.
The ambassadors hold little actual power, and can be fired.
Zimbabwe's government has not commented on Mr Mugabe's appointment, but the state-run Zimbabwe Herald newspaper called it a new feather in president's cap.
The southern African nation was once 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.