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With new infections reported around the world now surpassing those in mainland China, WHO director general Tedros Adhanom Ghebreyesus said even rich nations should prepare for surprises.
"No country should assume it won't get cases, that would be a fatal mistake, quite literally," Tedros said on Thursday, pointing to Italy, where authorities said three more people had died, bringing the toll from Europe's worst outbreak of the illness to 17. Confirmed cases there rose to 650.
There is no cure for the coronavirus, which can lead to pneumonia, and a vaccine may take up to 18 months to develop.
As well as stockpiling medical supplies, governments ordered schools shut and cancelled big gatherings, including sports events, to try to halt the flu-like disease that emerged in China more than two months ago from an illegal wildlife market.
It is on the decline there after an aggressive containment campaign, but rising elsewhere.
In Japan, where cases rose to 200, there is particular concern after a woman tested positive for the virus for a second time.
Second positive tests have also been reported in China and could imply contracting the disease does not confer immunity. Scientists warned that much remains unknown about the virus.
The head of the WHO's emergency programme, Dr Mike Ryan, said discussions were being held with organisers about the fate of the 2020 Olympics, scheduled for July in Tokyo, although no decision was expected soon.
The coronavirus has mainly battered China, causing more than 80,000 infections and around 2750 deaths. It has spread to another 44 countries, where around 3500 cases and 54 deaths have been reported.
A patient in the Netherlands on Thursday was diagnosed with coronavirus, health authorities said, the first confirmed case in the country. The patient in the southern city of Tilburg had recently travelled in northern Italy and was being treated in isolation.
Though the outbreak meets the definition of a pandemic - widespread contagion across a large region - the WHO has so far held back from using that term.
"This virus has pandemic potential," WHO chief Tedros told reporters in Geneva.
He said Iran, Italy and South Korea were at a "decisive point", still short of sustained community transmission, and that U.S. President Donald Trump was right to recommend preventive hygiene measures such as frequent hand-washing.
In Australia, Prime Minister Scott Morrison ordered hospitals to ensure sufficient medical and protective supplies and staff. Trump put Vice President Mike Pence in charge of America's response, while France's President Emmanuel Macron rallied the nation.
"We have a crisis before us. An epidemic is on its way," Macron said at a Paris hospital where a 60-year-old man this week became France's second coronavirus fatality.
Germany, too, has warned of an impending epidemic. And Greece, a gateway for refugees from the Middle East and beyond, announced tighter border controls.
MARKETS CONTINUE SLIDE
Spooked by the impact on China, the heart of corporate supply chains, and the increasing effect on other countries, stocks sank deeper into the red and oil prices fell.
Global equity markets have dropped for six straight days, wiping out more than $US3.6 trillion ($NZ5.7 trillion) in value.
Jeremy Farrar, a specialist in infectious disease epidemics and director of the Wellcome Trust global health charity, urged finance institutions to commit an initial $10 billion funds to fighting the virus.
"What we are really missing is tangible, high-level funding and support from global financial institutions," he said in a statement. "The possible impact of this coronavirus is far beyond a health emergency - it's a global crisis with potential to reach the scale of the global financial crisis of 2008."
Traders are betting the US Federal Reserve will move aggressively to cut borrowing costs in coming months in response to the effects of the coronavirus on the economy.
European Central Bank policymakers Isabel Schnabel and Klaas Knot expressed concern about the virus's spread, although Knot, a policy hawk, noted that China's economy had rebounded strongly after the 2002/03 SARS epidemic that also originated there.
Iran, urging people to avoid unnecessary travel, extended closures of cinemas, cultural events and conferences for another week and called off Friday prayers in some cities.
The WHO's Ryan said Iran's outbreak may be worse than yet realised. Twenty-six people have died there, the highest toll outside China, with 245 infected, including some senior officials, adding to the isolation of a nation already under US sanctions.
New cases in South Korea took its total to 1261 with 12 deaths.
Italy, desperate to stave off a probable recession, warned that the "epidemic of misleading information" could do worse harm than the virus itself.
The coronavirus has played havoc with global aviation and tourism as airlines cancel flights, countries ban visitors from hot spots and nervous passengers put off travel.
In Spain's Canary Islands, 130 of 700-plus guests locked down in a hotel were cleared to leave.
The United States is managing 59 cases - most Americans repatriated from a cruise ship quarantined in Japan where almost 700 cases developed. But Trump said the risk was "very low" in the United States which was "very, very ready".
Chinese authorities said the number of new deaths stood at 29 on Thursday, its lowest daily tally since Jan. 28. There were just 433 new cases in mainland China over the previous day, compared to 586 in nations and territories elsewhere.