The WHO leader faced criticism in the wake of the decision from the worldwide community and public figures in Zimbabwe, where Mugabe has been in power for 37 years and the public health system is rife with problems. "I will issue a statement as soon as possible", Tedros, a former Ethiopian health minister, said.
The UK government had led the criticism of the World Health Organization after it named Mugabe a "goodwill ambassador".
Critics claimed his policies and long record of alleged human rights abuses have had a disastrous impact on his country's health system.
An AFP report said that the WHO boss had faced mounting pressure to reverse the decision, including from some of the leading voices in global public health.
Britain said Mugabe's appointment as a goodwill ambassador for non-communicable diseases in Africa was "surprising and disappointing" and that it risked overshadowing the WHO's global work.
Mugabe, who has been in power since 1980, is in increasingly fragile health and makes regular trips overseas for medical treatment.
He said he revoked Mr Mugabe's position in the best interests of the WHO. He has also been blamed for a health crisis that has pushed doctors to strike and left hospitals without medicine.
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"Amid reports of ongoing human rights abuses, the tyrant of Zimbabwe is the last person who should be legitimised by a United Nations position of any kind", the group's executive director Hillel Neuer said in a statement.
Hillel Neuer, executive director of the Geneva-based group UN Watch, described Mugabe's appointment as "sickening".
Zimbabwe's government has not commented on Mugabe's appointment, but a state-run Zimbabwe Herald newspaper headline called it a "new feather in president's cap".
"The whole world knows what Mugabe has done on the health delivery of this once great country".
"We have registered our concerns with WHO Director General Dr. Tedros Adhanom Ghebreyesus", a foreign office spokesperson said in an email.
World Health Organization had earlier on Saturday pointed to Zimbabwe's record on tobacco, non communicable diseases (NCD) and Tedros' desire to engage senior politicians as justifications for the Mugabe honour.