The EU has sponsored a motion at Tuesday's session of the WHO's annual assembly to urge an "impartial, independent and comprehensive evaluation" of the worldwide response to the pandemic.
President Trump has threatened to withdraw the US from the group and permanently cut off all funding to the agency.
"We still have a long way to go in this pandemic", he said on Twitter.
China has said it is open to an independent inquiry - but only once the pandemic is over.
"In the last 24 hours, 106.000 new cases of coronavirus infection have been recorded in the world, which is the largest daily increase in the number of infected since the beginning of the pandemic", the WHO Director General said, adding that nearly two thirds of those cases were registered in four countries.
Washington said Taiwan's continued exclusion "further damages the WHO's credibility and effectiveness".
More than 4.9 million cases of the novel coronavirus have been registered in total since the outbreak first emerged in China last December, according to a tally from official sources compiled by AFP.
Reacting to the new numbers of cases of coronavirus, Trump said it is "a badge of honor" that the USA has the world's highest number.
The World Health Organization's (WHO) member states, including China and the US, have adopted a joint resolution for a prompt independent inquiry into the global health response to the Covid-19 pandemic, including the actions of the agency, as the 73rd annual World Health Assembly concluded. He alleged a series of missteps and kowtows to China that World Health Organization had made in its handling of the coronavirus pandemic.
Mr. Trump posted a four-page letter to his Twitter feed with the warning Monday evening and gave Mr. Tedros 30 days to make fundamental reforms.
Nonetheless, the US approved of the resolution's final draft, which included language pointing to the "leadership" of the World Health Organization in coordinating a global response to the Covid-19 pandemic.
Asked Wednesday when that might be, Tedros said: "When all the conditions we need are actually met". Only the United States and Russian Federation have counted more cases than Brazil has. "But it's also reminded us that for all our differences, we are one human race, and we are stronger together".
Brazil is the "most affected" South American country, and authorities there have approved broad use of the anti-malarial drug hydroxychloroquine for treatment of COVID-19, he said.
The two drugs are among a handful involved in WHO-coordinated clinical trials to find effective treatments for the disease.