World Health Organization Director-General Tedros Adhanom Ghebreyesus, who has presided during one of the biggest public-health crises in decades, appeared likely to lead the organization for a second five-year term, after a deadline for countries to nominate other candidates passed without any government presenting a challenger.

Dr. Tedros was backed by 28 governments, including France and Germany. The U.S., which had decided to leave the organization under former President Donald Trump but reversed that move under the Biden...

World Health Organization Director-General Tedros Adhanom Ghebreyesus, who has presided during one of the biggest public-health crises in decades, appeared likely to lead the organization for a second five-year term, after a deadline for countries to nominate other candidates passed without any government presenting a challenger.

Dr. Tedros was backed by 28 governments, including France and Germany. The U.S., which had decided to leave the organization under former President Donald Trump but reversed that move under the Biden administration, didn’t formally back him, nor did China, whose handling of the pandemic Dr. Tedros praised early on. The U.S. is the WHO’s biggest donor.

His home country of Ethiopia, which is currently at war with rebels from the same Tigrayan ethnic group as Dr. Tedros, also didn’t back his nomination.

The first African leader of the global public health agency, Dr. Tedros was in charge as the coronavirus pandemic began in China in late 2019. He found himself caught between Beijing and Washington as the two world powers traded blame for the spread of the disease.

His re-election wasn’t always certain, especially under Mr. Trump. More recently, China has expressed frustration with Dr. Tedros, after he called for an investigation into whether the virus escaped from a lab in Wuhan, the Chinese city that was the site of the first confirmed outbreaks in December 2019.

The Biden administration’s decision not to put forward a candidate is a missed opportunity, said Craig Singleton, an adjunct fellow at the Foundation for the Defense of Democracies, a foreign policy and national-security think tank in Washington. “The administration has put forward candidates for other international organization elections, such as the International Telecommunication Union, but has yet to provide an explanation for its decision to not challenge Tedros,” he said.

Dr. Tedros will undergo an interview in January with the WHO’s executive board, the agency said, to determine whether he still meets its criteria to lead the organization. The executive board is the WHO’s governing body. In May, governments will cast secret ballots to elect the next leader, whose term begins in August.

No other government put a candidate forward by the Sept. 23 deadline; any rival candidates would have been announced Friday.

“The World Health Organization needs strong, pragmatic and visionary leadership,” a letter from the German ambassador to the WHO said. The letter said that most European countries, including France and Spain, support his nomination for a second term in office.

Traditionally, it is rare for WHO director-generals to face competition for a second term. However, Dr. Tedros’s first term in office coincided with the Covid-19 pandemic, multiple Ebola outbreaks and an internal investigation into WHO employees who an agency report said committed rape and traded jobs for sexual favors in Democratic Republic of Congo.

The WHO also saw a debate over whether the coronavirus could have come from a lab in Wuhan and nearly saw the U.S. leave after the Trump administration argued that Dr. Tedros was being too deferential to China.

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A former foreign minister and former health minister of Ethiopia, Dr. Tedros took office after the agency’s slow response to West Africa’s 2014 Ebola outbreak sparked a move to react more quickly to emerging disease threats.

He quickly pushed for the WHO’s emergency panel to declare Covid-19 an international public health emergency within a month of the first reported cluster. He helped set up Covax, a program established to supply Covid-19 vaccines to poor countries.

It was Dr. Tedros’s close attention to the concerns of smaller and poorer countries that tipped the balance in his favor, said an ambassador to the WHO from the developing world, who felt that a rival would have struggled to win the support of countries that now depend on Covax for vaccines.

“Simply put, countries are happy because he continually engaged them, large and small,” the ambassador said. “He has led the organization through one of its toughest moments.”

At the same time, he was widely criticized at the beginning of the pandemic for effusively praising China publicly for its outbreak response, which included a lockdown of 60 million people. He took a different posture with China this year when he called for a deeper investigation into the origin of the pandemic.

He argued against the kinds of border restrictions that proved vital in helping countries like Vietnam and New Zealand avoid large-scale death tolls.

Under his leadership, the WHO initially opposed widespread mask usage, and didn’t recommend them until four months into the pandemic.

It was also slow to recognize that the virus could spread before causing symptoms, a finding that Asian governments realized within weeks of the first clusters. For months, its leaders argued that the virus was primarily spreading via large, heavy droplets; scientists in early 2020 found that talking, shouting or singing often expels the virus through tiny particles that linger in the air, a conclusion the WHO finally reflected in its guidelines in April 2021.

China and the U.S., meanwhile, repeatedly sparred over the agency’s efforts to understand the origins of the virus. China resisted international pressure for an investigation into Covid-19’s origins. It then delayed the WHO’s probe for months, secured veto rights over participants and insisted its scope encompass other countries as well.

The WHO was only able to send its team of experts to Wuhan in January—a year into the pandemic—after Dr. Tedros publicly expressed frustration with China’s delays.

Meanwhile, U.S. intelligence agencies have claimed the virus could have come from research facilities working with coronaviruses in Wuhan, a hypothesis that Dr. Tedros has offered to dispatch experts to investigate.

Under the circumstances, the WHO would have benefited from a contested election, which would have forced its leadership to reckon with the agency’s shortcomings, said Lawrence Gostin, faculty director of the O’Neill Institute for National and Global Health Law at Georgetown University.

“The WHO is often called the world’s health democracy but this is not democratic, it is not healthy,” he said. “It’s not as if everything has gone smoothly with the WHO during this pandemic. There’s been controversy over the origins, scientific confusion over aerosol transmission and masks. He’s done an extraordinarily good job in extraordinarily difficult circumstances but there ought to be a full and open debate about the WHO’s future.”

Write to Drew Hinshaw at drew.hinshaw@wsj.com and Betsy McKay at betsy.mckay+1@wsj.com