More than a dozen foreign scientists led by the World Health Organization gathered with Chinese counterparts last month to vote on the question: How did the Covid-19 pandemic start? The show of hands came after a four-week joint study in the city where the first cases were identified, a mission many hoped would provide some clarity to a world craving answers.

For a while, it appeared to. The vote’s results captured headlines: The virus probably jumped to humans from an animal; further research was needed on whether it spread on frozen food; a lab leak was “extremely unlikely.”

A month on, however, as the WHO-led team finalizes its full report on the Wuhan mission, a Wall Street Journal investigation has uncovered fresh details about the team’s formation and constraints that reveal how little power it had to conduct a thorough, impartial examination—and call into question the clarity its findings appeared to provide.

China resisted international pressure for an investigation it saw as an attempt to assign blame, delayed the probe for months, secured veto rights over participants and insisted its scope encompass other countries as well, the Journal found.

Meanwhile, the Trump administration’s early assertions that the virus may have come from a Chinese laboratory soured diplomatic efforts to press China to allow a more rigorous probe. Many scientists view a lab accident as an unlikely cause of the pandemic, arguing the chances are greater that it jumped to humans and began spreading in nature. Then, the administration began withdrawing from the WHO, making it harder to rally allies. A Trump spokeswoman declined to comment.

U.S. officials said they asked, unsuccessfully, for the WHO to consult its governing body on negotiations with China over details of the probe, and said Washington lacked clarity on how the international team was recruited. The team members said they didn’t have the mandate, expertise and access to investigate a potential lab leak. And the team reached its verdict on Feb. 8 in a show of hands with Chinese counterparts, many of whom report to a government that had already ruled out a lab accident and which has suggested the pandemic began outside China.

WHO spokesman Tarik Jasarevic said China didn’t weigh in on the agency’s selection of team members or object to any who had been chosen. The mission was mandated to design and recommend scientific studies, not to do an investigation, let alone a forensic audit of laboratories, WHO officials said. The WHO normally negotiates the terms of such missions with a host government directly, without other member states, Mr. Jasarevic said.

The upshot: What should have been a timely collaborative scientific inquiry has become slower, harder and more opaque. The world now risks never finding an answer to the virus’s origins.