A leading candidate to head the World Health Organization was accused this week of covering up three cholera epidemics in his home country, Ethiopia, when he was health minister — a charge that could seriously undermine his campaign to run the agency.

The accusation against Tedros Adhanom Ghebreyesus was made by a prominent global health expert who is also an informal adviser to Dr. David Nabarro, a rival candidate in the race for W.H.O. director general.

Dr. Tedros, who uses his first name in his campaign, denied the cover-up accusation and said he was “not surprised at all but quite disappointed” that Dr. Nabarro’s camp — which he said included high-ranking British health officials — had switched to running what he called a “last-minute smear campaign.”

The vote for the next director general of the W.H.O. is to take place at a weeklong meeting of the world’s health ministers in Geneva beginning May 22.