Pompeo also criticized China's scientific laboratories, implying that they do not have "proper handling" and he openly questioned whether the coronavirus that has caused the COVID-19 pandemic originated in a lab in Wuhan -- the city that was the epicenter of the outbreak.
It's a charge that has been floating for weeks now, with Trump saying Friday that the U.S. was "looking at it. It seems to make sense."
Last month, a study published in the scientific journal Nature Medicine analyzed the available evidence and determined the novel coronavirus "is not a laboratory construct or a purposefully manipulated virus," with the researchers concluding, "We do not believe that any type of laboratory-based scenario is plausible."
But the report also seemed to dismiss the Chinese government's claim that it originated at a wet market in Wuhan, a provincial capital of 11 million people.
"Our analyses, and others too, point to an earlier origin than that. There were definitely cases there, but that wasn't the origin of the virus," Dr. Robert Garry, a professor at Tulane University School of Medicine and one of the authors, told ABC News at the time.
While scientists race to discover the virus' origins, it has in the meantime become a political football between the U.S. and China, particularly after Chinese officials spread disinformation that the U.S. military unleashed the virus in Wuhan last fall.
China's Foreign Ministry again asserted the government had been transparent, with spokesperson Geng Shuang saying Wednesday, "China has regularly informed the U.S. of the epidemic since January 3. The U.S. side has ready access to relevant information and data from China."
But Pompeo said China violated WHO's international health regulations by failing to notify the U.N. agency within 24 hours of a possible public health emergency of international concern after cases of a new viral pneumonia appeared in late 2019. He also accused Beijing of failing to provide timely updates on the outbreak to WHO -- another violation.
China "covered up how dangerous the disease is. It didn't report sustained human-to-human transmission for a month until it was in every province inside of China. It censored those who tried to warn the world in order to halt the testing of new samples and it destroyed existing samples," Pompeo said.
But the Trump administration has not taken steps to punish China, with Pompeo saying repeatedly it is not the time for "recriminations."
In contrast, the administration has gone after the World Health Organization and put a "halt" on funding from the U.S., which provides more funding than any other government.
Just two weeks ago, Pompeo said those funds "protect Americans and keep us safe." But on Wednesday, his director of foreign assistance at the State Department James Richardson said the administration is "pausing all assistance for 60 to 90 days" while it searches for new partner organizations to provide with global health funding.
"For every contract or every dollar flowing today, we're just taking WHO off the table, and we're going to provide that assistance to these other organizations in order to get the job done," Richardson said.
A senior administration official said that for fiscal year 2020, which started last October, the administration had already provided about half of the U.S. contribution, but approximately $65 million was now being withheld.
The U.S. also provides hundreds of millions of dollars each year for particular initiatives or crises to WHO, including polio, HIV/AIDS and Ebola. The senior official said that amounted to $300-400 million and would also be halted.
U.S. Agency for International Development and the State Department did not respond to requests for details. But Dr. Mike Ryan, WHO's executive director for health emergencies program, said Wednesday the pause will hit WHO's non-COVID-19 programs, such as immunizing children, eradicating polio, and assisting vulnerable populations.
Trump's halt to WHO funding has been widely panned, including by lawmakers, allied countries and public health experts. But some experts says the grounds Pompeo put forth Wednesday were also shaky.
"The IHRs (international health regulations) put all of the onus on the member state, not on WHO. A member state has an obligation to promptly notify WHO of novel events, but the IHRs don't give WHO the authority to compel that," according to Jeremy Konyndyk, a senior fellow at the Center for Global Development.
Pompeo blamed WHO for failing its "continuing obligation to make sure that those rules are being complied with" and said its director-general has "enormous authority with respect to nations that do not comply."
But WHO has no authority to compel data, with its bylaws permitting it only to share information given by a country and with its consent. There's an exemption if the country itself is completely stonewalling, but only when it's "justified by the magnitude of the public health risk," and in this case, China was at least "going through the motions of cooperating," according to Konyndyk.
"This might sound frustrating, but flip it around: How would the U.S. government react if WHO told us they were opening a unilateral investigation in our country?" tweeted Konyndyk.
Beyond the initial response, Pompeo accused China of continued obfuscation -- and seemed to give credence to the theory that the virus first jumped from an animal to a human in one of Wuhan's labs.
"We still do not have a sample of the virus, nor has the world had access to the facilities or other locations where the virus may have originated in Wuhan," Pompeo told reporters Wednesday -- demanding China grant access to labs across the country and casting doubt on whether virus samples are "being handled in a safe and secure way such that there isn't accidental release."
A State Department cable leaked to a Washington Post columnist stated the U.S. had concerns about safety at a Wuhan Institute of Virology lab when U.S. officials visited in 2018. The State Department declined to comment to ABC News, citing the privacy of diplomatic cables.
Shi Zhengli, the director of the lab, which studies deadly pathogens including coronaviruses found in bats, has denied that the first human transmission -- what's known as zoonotic spillover -- came from her lab and defended her scientists' safety record.
Even if there were safety issues, it would be difficult for a virus sample to "spill over" and infect a human in such a way that it was now contagious and started an outbreak, according to several health experts.
"It's a possibility, but it's an unlikely probability because the laboratory is a controlled setting and people wear personal protective equipment. I've seen hearsay that they maybe didn't have enough or they weren't skilled enough, but there are barriers, huge barriers between people and viruses in the laboratory setting," said Dr. Christine Johnson, director of the U.S. Agency for International Development's Predict project, which for over 10 years has studied viruses in animals and prepared local partners around the world to detect that kind of "spillover."
The probability of infection "is so much higher in the real world, where there are more people and more bats. It's vastly more likely than the potential for a human-bat interaction in the lab," added Johnson, who is also a professor of epidemiology and ecosystem health at UC Davis School of Veterinary Medicine and director of its EpiCenter for Disease Dynamic.
Dr. Peter Daszak, who worked more directly with Chinese labs as part of Predict, did not respond to ABC News' request for comment, but told the Wall Street Journal on Tuesday, "All the elements of the conspiracy are there if you want to believe it," but, "it's not true."
Instead, it is believed that the virus' mutation that makes it so contagious is much more likely to have happened spontaneously in nature, according to two new studies which were substantiated by Dr. Garry's team, and found that in a lab setting, that particular mutation gets "deleted" when the virus is passed in cell cultures. Their work on the virus continues, but it still has not killed the spread of countering conspiracy theories.
ABC News' Kate Holland, Jordyn Phelps and Christine Theodorou contributed to this report.