Coronavirus death tolls have climbed by more than 800 in both Italy and Spain but the World Health Organisation's emergency chief says cases in the two countries are "potentially stabilising".
In the United States, New York's governor issued an urgent appeal for medical volunteers from across the country amid a "staggering" number of deaths from the virus, saying: "Please come help us in New York, now."
Governor Andrew Cuomo's call came as the state's death toll climbed by more than 250 in a single day to a total of more than 1200 victims, most of them in the city.
He said an additional one million health workers were needed to tackle the crisis.
"We've lost over 1000 New Yorkers," Cuomo said. "To me, we're beyond staggering already. We've reached staggering."
Even before the governor's appeal, close to 80,000 former nurses, doctors and other professionals in New York were stepping up to volunteer, and a Navy hospital ship, also sent to the city after September 11, 2001, had arrived with 1000 beds to relieve pressure on overwhelmed hospitals.
The spike in deaths in New York was another sign of the long fight ahead against the global pandemic, which was filling Spain's intensive care beds to capacity and shutting millions of Americans inside even as the crisis in China, where the outbreak began in December, kept easing.
More than 235 million people - about two of every three Americans - live in the 33 states where governors have declared statewide orders or recommendations to stay home.
In California, officials put out a similar call for medical volunteers as coronavirus hospitalisations doubled in the past four days and the number of patients in intensive care tripled.
"Challenging times are ahead for the next 30 days and this is a very vital 30 days," President Donald Trump told reporters.
"The more we dedicate ourselves today, the more quickly we will emerge on the other side of the crisis."
In Europe, meanwhile, hard-hit Italy and Spain saw their death tolls climb by more than 800 each but the World Health Organisation's emergency chief said cases there were "potentially stabilising".
At the same time, Dr Michael Ryan warned against letting up on tough containment measures.
Three-quarters of a million people worldwide have become infected and more than 37,000 have died, according to a count by Johns Hopkins University.
The US reported more than 160,000 infections and more than 2900 deaths, with New York City the nation's worst hotspot but New Orleans, Detroit and other cities also seeing alarming clusters.
Dr Anthony Fauci, the US government's top infectious disease expert, warned smaller cities were likely about to see cases "take off" the way they had in New York City.
Italy's death toll climbed to nearly 11,600 but newly released numbers showed a continued slowdown in the rate of new confirmed cases and a record number of people recovered.
Bells tolled in Madrid's deserted central square and flags were lowered in a day of mourning as Spain raced to build field hospitals to treat an onslaught of patients. The death toll topped 7300.
In Japan, officials announced a new date for the 2020 Tokyo Olympics - summer of 2021 - as a spike in reported infections fuelled suspicions the government had been understating the extent of the country's outbreak while it was still hoping to salvage the Games.
Moscow locked down its 12 million people as Russia braced for sweeping nationwide restrictions.
Israel said Prime Minister Benjamin Netanyahu was quarantining himself after an aide tested positive for the virus.
In Britain, Prince Charles ended his period of isolation after testing positive for the virus and was in good health, his office said.
The crisis in China, where the outbreak began in late December, has eased although the mainland reported on Tuesday a rise in new confirmed cases, reversing four days of declines, due to an uptick in infections involving travellers arriving from overseas.
The city at the centre of the disaster, Wuhan, has begun reopening for business after authorities lifted more of the controls that locked down tens of millions of people for two months.
Australian Associated Press