The UN agency said while it is not calling the virus outbreak a pandemic just yet, it maintains that cases of COVID-19 have the potential to spread freely across the globe.
The World Health Organization on Monday said the new coronavirus epidemic had "peaked" in China but warned that a surge in cases elsewhere was "deeply concerning" and all countries should prepare for a "potential pandemic."
WHO chief Tedros Adhanom Ghebreyesus said the peak in China occurred between 23 January and 2 February and the number of new cases there "has been declining steadily since then.
"This virus can be contained," he told reporters in Geneva, praising China for helping to prevent an even bigger spread of the disease through unprecedented lockdowns and quarantines in or near the outbreak's epicentre.
An acceleration of cases in other parts of the world has prompted similar drastic measures. Italy has locked down 11 towns and South Korea ordered the entire 2.5 million residents of the city of Daegu to remain indoors.
It also caused falls of more than 3.0-percent in several European stock markets - with Milan plunging 5.4 percent - and a boost for safe-haven gold amid fears the epidemic could hit a global economic recovery.
The spread of the disease - officially known as COVID-19 - continued unabated with Afghanistan, Bahrain, Iraq, Kuwait and Oman announcing their first cases on Monday.
“Does this virus have pandemic potential? Absolutely, it has. Are we there yet? From our assessment, not yet,” the WHO chief said.
China has continued its preventive measures against the virus, on Monday postponing its agenda-setting annual parliament meeting for the first time since the Cultural Revolution in the 1960s.
In Iran, the death toll climbed on Monday by four to 12 - the highest number for any country outside China.
But there were concerns the situation might be worse than officially acknowledged. The semi-official ILNA news agency quoted one local lawmaker in hard-hit Qom - a religious centre - who said 50 people had died there.
The Iranian government denied the report, and pledged transparency.
Even so, authorities have only reported 64 infections in Iran, an unusually small number that would mean an extremely high mortality rate.
In China, 2,592 people have died out of 77,000 infections.
Michael Ryan, head of WHO's health emergencies programme, said a team from the UN agency would be arriving in Iran on Tuesday.
But he cautioned against drawing any conclusions about the mortality rate. Iran "may only be detecting severe cases" because the epidemic was still at an early stage, he said.
"We need to understand the exact dynamics of what has happened in Iran, but clearly there have been gatherings for religious festivals, and then people coming and then moving afterwards," he said.
Avoid 'public panic'
South Korea reported 60 more novel coronavirus cases on Tuesday, the smallest increase for four days in the Korea Centers for Disease Control and Prevention's morning updates.
The country now has 893 cases, the KCDC said - the largest national total anywhere outside China - adding one more person had died, taking the toll to eight.
For the previous three days, KCDC had reported triple-digit increases each morning as the outbreak took hold in South Korea, the world's 12th-largest economy.
As part of the containment efforts, school holidays were extended nationally while the 2.5 million people of Daegu were told to remain indoors.
Most of the country's infections are linked to the Shincheonji Church of Jesus in Daegu, an entity often accused of being a cult.
Shincheonji claims its founder, Lee Man-hee, has donned the mantle of Jesus Christ and will take 144,000 people with him to heaven on the day of judgement.
A 61-year-old female member developed a fever on February 10, but attended at least four church services before being diagnosed.
Authorities in Hong Kong announced that from Tuesday it would not allow arrivals from South Korea other than returning residents.
Mongolia earlier announced it would not allow flights from South Korea to land.
Speaking in Geneva, South Korean Foreign Minister Kang Kyung-hwa warned governments against taking action that would fan public panic.
"I am deeply concerned at incidents of xenophobia and hatred, discriminatory immigration controls and arbitrary repatriation," she said.
Football, fashion curbed
Fears were also growing in Europe, with Italy reporting four more deaths Monday, bringing the total to seven.
More than 200 people have been infected there, and several Series A football games were postponed over the weekend.
The famed Venice Carnival was also cut short, and some Milan Fashion Week runway shows were cancelled.
More than 50,000 people in about a dozen northern Italian towns have been told to stay home, and police set up checkpoints to enforce a blockade.
Prime Minister Giuseppe Conte has said that residents could face weeks of lockdown.
The virus is taking an increasingly heavy toll on the global economy, with many factories in China closed or subdued due to the quarantines.
The International Monetary Fund warned Sunday that the epidemic was putting a "fragile" global economic recovery at risk, while the White House said the shutdowns in China will have an impact on the United States.
Bruce Aylward, leader of an international mission of experts, said it was time for China to start lifting some of the restrictions.
"Obviously they want to get society back to a more normal semblance of what probably is the new normal, because this virus may be around... for months," Aylward said.