"We'll have to ask the hard questions about how it came about and how it couldn't have been stopped earlier," Britain's Foreign Secretary Dominic Raab said.
"There are clearly things that have happened that we don't know about," French President Emmanuel Macron said.
Trump's presidential campaign is running ads on the blame-China theme. The New York Times reports that the Republican Party sees it as an election strategy. The Democrats are taking the line that Trump has been too soft on China.
US officials have talked up a theory that the virus escaped a lab in Wuhan, although scientific analysis has pointed to wildlife being the source.
Trump previously accused the World Health Organisation of being "China-centric" as he cut US funding to the agency.
The WHO issued its first public warning about the mystery virus in the first week of January. Then, on January 14, a WHO official told reporters there was "the possibility of human-to-human transmission between people" and "there's also the possibility of super-spreading events".
Last week, AP reported that between January 14 and 19, top Chinese officials knew they were facing a pandemic. President Xi Jinping warned the public on January 20 but by then, AP reported, "more than 3000 people had been infected during almost a week of public silence".
In China, health workers and local officials are not allowed to release information on a disease emergency before the Ministry of Health, the ABC reports.
Can China's actions be blamed for the severe damage caused in some countries or were there enough warnings and time to limit the fallout? Variations in outcomes appear to relate to how quickly and decisively countries reacted.
The Sars animal virus epidemic of 2002-2003 originated in China and affected 26 countries. This time, even as Hong Kong, Taiwan, Singapore and South Korea quickly took protective action in January, nations further afield failed to bolster their defences. An ability to manufacture protective health equipment in an emergency will surely be part of many future national pandemic plans.
There's little doubt that Chinese authorities were less transparent than they could have been, dithered early on as crowds still congregated, and have not fully accounted for all victims of the coronavirus.
However, those charges can also be levelled at other countries.
For instance, Trump said that China must have the most deaths from the virus of any country despite its official figures. Regardless, it's believed that death tolls are also under-counted in both Europe and the US.
Many elderly people died without being tested or taken to hospital. Officials will get a clearer picture when data allows a comparison of this year's figures with mortality averages.
Not much understanding is extended to China despite it being the first country to face the new virus – which scientists are still learning about - in a heavily populated area, while having to deal with a multitude of organisational issues including compiling data on the victims. Other countries were able to watch and learn.
On the question of transparency, Trump spent much of January and February downplaying the virus threat but has since tried hard to deny he did so despite video evidence. While governors and health professionals complained about insufficient tests and equipment, the President kept saying that adequate capacity was there or on its way.
And Britain is a prime example of a country which wasted time as its citizens mingled.
It had its first two Covid-19 cases at the end of January. A new Sunday Times investigation outlined UK government missteps in February which included Prime Minister Boris Johnson missing five meetings on the virus. Warnings from scientists and calls to order health protective gear were reportedly ignored.
Britain brought in non-voluntary measures after other European countries. The closure of pubs and eateries on March 20 came after 140 deaths and 3200 cases.
Mistakes on handling the pandemic have not been confined to China.
