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President Donald Trump has heaped further criticism on China over its handling of the coronavirus outbreak, questioning the accuracy of its official death toll and saying he was looking into an unverified theory that the infection originated in a Chinese laboratory.

"Do you really believe those numbers in this vast country called China. … Does anybody really believe that?" Trump said when asked at the White House daily news briefing Wednesday why the U.S. has the highest numbers of official coronavirus deaths and cases in the world.

"Some countries are in big, big trouble and they're not reporting the facts — and that's up to them," he said.

The comments were the latest in a growing series of attacks on Beijing by the president, who has referred to the outbreak as the "China virus."

A day earlier Trump said he would stop funding the World Health Organization, accusing it of helping China cover up the outbreak, a move that outraged world leaders and experts.

A man is tested for COVID-19 in Wuhan on Thursday. Hector Retamal / AFP - Getty Images

According to official statistics, the United States has 634,000 confirmed cases and 32,000 deaths. China — whose population is more than four times that of the U.S. — says it has around 82,000 cases and 3,300 deaths.

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Many countries have struggled to roll out enough tests, meaning that across the world the number of documented cases and fatalities is likely lower than the real figure.

But some have viewed with particular suspicion the death toll announced by China, a one-party state that watchdogs accuse of a lack of transparency. It kept the SARS epidemic of 2002-03 that killed nearly 800 of its people secret for weeks.

Others have also questioned whether China has been reporting all of its COVID-19 cases and deaths, which official figures show have flattened in recent weeks.

Michael Gove, a senior minister in the British government, told the BBC in late March that "some of the reporting from China was not clear about the scale, the nature, the infectiousness of this."

Local officials in Wuhan, the city where the outbreak was first recorded, have been accused of attempting to cover up the severity of the disease in its early stages, even reprimanding a doctor who tried to warn them.

Chinese Premier Li Keqiang, who has been coordinating the country's coronavirus response, went as far to warn local officials not to "cover up" or "under report" new infections when travel restrictions were relaxed in Hubei province at the end of March.

Chinese commuters in Beijing on Wednesday, April 15, 2020. Kevin Frayer / Getty Images

On Wednesday, Trump was also asked about media reports concerning safety standards at a virology lab in Wuhan.

The reports, which have not been verified by NBC News, suggest the outbreak could have been caused by a naturally occurring virus transmitted to a lab staffer by mistake.

"More and more, we're hearing the story, and we'll see," Trump said. "We are doing a very thorough examination of this horrible situation that happened."

In response, Chinese Foreign Ministry spokesman Zhao Lijian said that "many well-known medical experts in the world also think that the statement of so-called laboratory leaks is without scientific basis."

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Trump has not always been so critical of China, and in fact spent much of January and February praising the country's efforts to combat the coronavirus. On Feb. 29 he remarked how Beijing was "making tremendous progress" containing the outbreak.

This follows a pattern that started long before the contagion gripped the world.

Trump has for years often praised his counterpart, Chinese President Xi Jinping, while Washington and Beijing engaged in a tit-for-tat trade war, and tensions flared over China's territorial claims in the South China Sea.