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4 year oldThe letter outlines a 30-day deadline for the body to commit to "substantive improvements" or risk losing millions and US membership altogether.
Addressed to WHO chief Tedros Adhanom Ghebreyesus, it criticises stages of the body's response since December.
Earlier on Monday, Mr Trump called the UN's health body a "puppet of China".
The president, who faces re-election this year and has himself been criticised for his handling of the pandemic, has blamed China for trying to cover up the outbreak and has accused the WHO of failing to hold Beijing to account.
Chinese foreign ministry spokesman Zhao Lijian said Mr Trump was trying to mislead the public, smear China and "shift the blame for [the US's] own incompetent response".
The US has more than 1.5 million of the world's 4.8 million confirmed cases of coronavirus so far, with more than 90,000 deaths.
Mr Trump's ultimatum also comes at a time of pressure for the WHO.
On Monday Dr Tedros backed a review of the agency's handling of the pandemic. He said an independent evaluation would take place "at the earliest appropriate moment".
Mr Trump published the letter on Twitter on Monday night, following a day of heavy US criticism of the health agency.
Health Secretary Alex Azar spoke at the WHO's World Health Assembly and accused the organisation of letting Covid-19 spin "out of control" at the cost of "many lives".
In his letter to Dr Tedros, the US president accuses the WHO of having an "alarming lack of independence" from China.
Among his assertions, Mr Trump accuses the agency of having "consistently ignored" what he describes as "credible reports" of the virus spreading in Wuhan at the start of December or even earlier.
This is the letter sent to Dr. Tedros of the World Health Organization. It is self-explanatory! pic.twitter.com/pF2kzPUpDv
— Donald J. Trump (@realDonaldTrump) May 19, 2020
Beijing denies the allegation. Earlier this month, the Chinese foreign ministry said the country had "all along been in good communication and co-operation" with the WHO and had "never attempted to manipulate the organisation".
Also in the letter, Mr Trump:
Mr Trump, in his conclusion, alleges that "repeated missteps" by Dr Tedros and the WHO had been "extremely costly for the world".
"The only way forward for the World Health Organization is if it can actually demonstrate independence from China," his letter says.
Mr Trump then calls for the organisation to commit to "major substantive improvements" within 30 days, without clarifying what this means.
Without these changes, the president says, the US will make his temporary freeze of US funding permanent and "reconsider our membership in the organisation" altogether.
Mr Trump announced the halting of US payments last month. The country is the largest single contributor to the WHO, accounting for just less than 15% of its funding in the past financial year.
The president is seeking a second presidential term in November, and his attacks on China are seen as part of his re-election strategy.
President Trump is not alone in criticising the WHO's response. The organization has been accused of being too trusting of China, and overly praising the country for its approach to the outbreak as it punished whistleblowers who tried to raise the alarm.
One WHO tweet from January quoted Chinese investigators saying there was "no clear evidence of human-to-human transmission" of the virus. It released a statement the following week saying this did in fact seem to be taking place in Wuhan.
The UN agency has also been criticised for the time it took to declare coronavirus a global health emergency.
Dr Tedros strongly defended the organization told reporters earlier this month that "didn't waste time".
On Monday, however. he agreed to an independent review of the WHO's actions.
These issues have dominated the two-day World Health Assembly in Geneva - the annual meeting of member states reviewing the WHO's work - which is scheduled to end on Tuesday.
Also at issue is a resolution which would allow poorer countries access to any coronavirus vaccines or treatments that could be developed by private manufacturers.
President Xi said on Monday that any vaccine developed in China would "be made a global public good".
The Financial Times newspaper reports that the US is planning to publicly distance itself from some of the wording in the resolution. It is expected to pass despite any US objections.
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