US Secretary of State Mike Pompeo has claimed that "enormous evidence" showed the new coronavirus originated in a laboratory in China, further fuelling tension with Beijing.
Europe and parts of the US prepared to cautiously lift lockdowns as signs emerge that the deadly pandemic is ebbing and governments look to restart their battered economies.
More than 246,000 people have been killed and 3.5 million infected worldwide by the virus.
It has left half of humanity under some form of lockdown and pushed the global economy towards its worst downturn since the Great Depression.
US President Donald Trump, increasingly critical of how China managed the first outbreak in the city of Wuhan in December, last week claimed to have proof it started in a Chinese lab but said he was not allowed to reveal it.
Scientists believe the virus jumped from animals to humans, after emerging in China, possibly from a market in Wuhan selling exotic animals for meat.
Mr Trump, without giving details, said on Thursday that he had seen evidence the Wuhan Institute of Virology was the source, appearing to repeat rumours fuelled by US right-wing radio commentators about a secret lab.
China denies the claims and the US Director of National Intelligence's office said analysts were still examining the exact origin of the outbreak.
Mr Pompeo, a former CIA chief, told the ABC on Sunday that he agreed with the US intelligence community about the "wide scientific consensus that the Covid-19 virus was not man-made or genetically modified".
But he spoke of "significant" and "enormous" evidence that the virus originated in a Wuhan lab.
"I think the whole world can see now," Mr Pompeo said. "Remember, China has a history of infecting the world and running substandard laboratories."
Mr Pompeo said early Chinese efforts to play down the coronavirus amounted to "a classic Communist disinformation effort that created enormous risk".
"President Trump is very clear: we'll hold those responsible accountable," he said.
US news reports say Mr Trump has instructed intelligence to find out more about the origins of the virus, as he makes China's handling of the pandemic a centrepiece of his campaign for the November presidential election.
The US has the most coronavirus deaths in the world, at more 68,000, and Mr Trump is keen for a turnaround to help reduce the harm to the economy, with tens of millions left jobless.
Florida is set to ease its lockdown on Monday, as other states wrestle with pressure from demonstrators, some armed, who have rallied against the restrictions.
There are signs the pandemic is slowing in some parts of the US.
In New York, the hardest hit in the US outbreak, an emergency field hospital built in Central Park is set to close as virus cases decline.
European nations are also preparing for cautious easing of restrictions.
Hard-hit Italy, which reported its lowest daily toll since lockdown orders were imposed on March 10, is set to follow Spain in letting people outside.
Italians from Monday will be allowed to stroll in parks and visit relatives.
Restaurants can open for takeaways and wholesale stores can resume business, but there was some confusion over the rules.
Romans were doing aerobics on rooftop terraces and exercising indoors while squares in the city centre were mostly empty on the last day Italians were obliged to remain within 200 metres of their homes.
"On the one hand, we're super excited for the reopening," said Rome resident Marghe Lodoli, who has three children.
"We're already organising various activities the kids will be able to do with their grandparents outdoors.
"On the other hand, it's disorientating. The rules are not clear and we're not sure if just using common sense will do."
Italian authorities have said some preventive measures are still needed in a country with the second-highest number of virus deaths.
Germany will continue its easing on Monday, while Slovenia, Poland and Hungary will allow public spaces and businesses to partially reopen.
Portugal will also begin to ease some of its lockdown measures on Monday, allowing small shops and hairdressers to reopen, but people must still observe strict social distancing.
In another sign of life returning to normal, a German minister said on Sunday that he supported a resumption of the country's football season this month, as long as teams respected hygiene conditions.
The British government said the easing of coronavirus lockdown measures was likely to be gradual, as it announced a further rise in the overall death toll.
Prime Minister Boris Johnson was expected to unveil the government's plans in coming days, after announcing the country had passed the peak of the virus.
Most governments are sticking to measures to control the spread of the virus, including social distancing and masks in public, and more testing to try to track infections as they relax curbs.
Face masks will be mandatory on public transport starting Monday in Spain, where people were allowed to go outdoors to exercise and walk freely on Saturday after a 48-day lockdown.
Even as some European countries gradually lift restrictions, officials in Moscow urged residents to stay home.
With cases increasing by several thousand each day, Russia now has a higher rate of new infections than any European state.
European leaders are backing an initiative from Brussels to raise €7.5 billion (Dh30.23bn/US$8.3bn) to tackle the pandemic and raise funds for efforts to find a vaccine for Covid-19.
The race is on to find a viable vaccine or treatment with several countries involved in trials.
Meanwhile in Asia, South Korea, once the second worst-hit nation, said on Sunday it would ease a ban on some gatherings and events provided people "follow disinfection measures".
Thailand allowed businesses such as restaurants, hair salons and outdoor markets to reopen if social distancing were maintained and temperature checks carried out.
But experts caution that many countries are still not through the worst.
The Philippines suspended all flights into and out of the country for a week starting on Sunday to try to ease pressure on its congested quarantine centres.
Iranian President Hassan Rouhani announced mosques would reopen across large parts of the country, after they were closed in early March to try to contain the Middle East's deadliest outbreak.
But Mr Rouhani said that while Iran would reopen "calmly and gradually", it should also prepare for "bad scenarios".