Trump issued the stark warning in a letter he posted on Twitter, accusing the organization of ignoring reports of the novel coronavirus spreading in China in December and failing to share "critical information" regarding the outbreak.
In his letter, Trump said the only way forward for the body was if it could demonstrate independence from China, adding that his administration had already started reform discussions with Dr Ghebreyesus.
"I look at that as, in a certain respect, as being a good thing because it means our testing is much better", he said on Tuesday at the White House as he hosted his first Cabinet meeting since the COVID-19 outbreak began.
The letter also addressed the political "gamesmanship" of the World Health Organization during an apolitical global pandemic.
The president said he would not allow funding to an organisation that does not serve USA citizens interests.
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And this year, Washington has already paid the World Health Organization about $58 million, senior Trump administration officials said last month, half of what it is required to pay for 2020 - known as an assessed contribution. "China calls on the global community to increase political and financial support for World Health Organization so as to mobilize resources worldwide to defeat the virus", he said.
"You also strongly praised China's strict domestic travel restrictions, but were inexplicably against my closing of the United States border, or the ban, with respect to people coming from China", the letter read.
A resolution drafted by the European Union called for an independent evaluation of the WHO's performance and appeared to have won consensus backing among the health body's 194 states.
Across Europe, world leaders and health ministers used their messages to back an investigation, but also to reiterate their support for the World Health Organization and its importance, as well as the need for a united and collective global response.
"The US leadership's open letter is full of vague expressions such as probably etc", Zhao said.
The WHO has not publicly criticized the United States ban on travel from China.
"We call on the worldwide community to enhance political and funding support for WHO" in order to defeat the virus, he said.