5-6 minutes - Source: BBC
The 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.
China has repeatedly denied the allegations, arguing the country had released information "in an open, transparent, responsible and timely manner".
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".
What does the letter say?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.
The US president has repeatedly accused China of failings in its response to the coronavirus outbreak.
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:
- Cites reports that the WHO delayed an emergency declaration under pressure from President Xi Jinping
- Criticises the agency's praise of China's "transparency" amid reports of censorship and lack of international co-operation
- Accuses the WHO of failing to comment on virus-related racial discrimination allegedly happening within China
- Says Dr Tedros could have saved "many lives" if he had acted more like Dr Harlem Brundtland, the WHO chief during the Sars outbreak of 2003
"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 World Health Assembly, the annual meeting of member states reviewing the WHO's work, is being held over two days, ending on Tuesday.
So far the virtual forum has been dominated by clashes over the organisation's role, as well as pushes for an inquiry into the handling of the pandemic.