Hong Kong (CNN) The United States and other countries issued strict travel restrictions for foreign nationals who traveled to China as the number of deaths from the Wuhan coronavirus outbreak continued rising on Friday.

A day after the World Health Organization (WHO) declared the virus a global health emergency , Chinese authorities reported 45 deaths, all of them in Hubei, the province at the center of the outbreak of which Wuhan is the capital, bringing the total death toll across the country to 258.

As of Friday, there were more than 10,000 coronavirus cases confirmed in China, authorities said, an increase of over 2,000 from the previous day. That surpasses the 2003 severe acute respiratory syndrome (SARS) outbreak that began in southern China, which infected 8,098 people worldwide, killing 774.

More than 20 countries and territories outside of mainland China have confirmed cases of the virus -- spanning Asia, Europe, North America and the Middle East -- as the United Kingdom reported its first two cases on Friday.

On Friday, President Donald Trump signed a proclamation suspending the entry of foreign nationals who have traveled in China in the last two weeks and could pose a risk of spreading the virus, Health and Human Services Secretary Alex Azar said.

Foreign nationals who are the immediate family of US citizens or permanent residents are exempt. US citizens returning to the United States who have been in China's Hubei province in the two weeks before their return will be subject to up to 14 days of mandatory quarantine, Azar said.

The decision by the WHO prompted governments to upgrade their own response to the virus, with the US State Department raising its travel advisory for China to it's highest level: Do not travel.

The WHO defines a public health emergency of international concern as "an extraordinary event" that constitutes a "public health risk to other States through the international spread of disease," and "to potentially require a coordinated international response." Previous emergencies have included Ebola, Zika and H1N1.

Ghebreyesus, who met this week with Chinese President Xi Jinping, said the WHO "continues to have confidence in China's capacity to control the outbreak."

"We would have seen many more cases outside China by now -- and probably deaths -- if it were not for the government's efforts," he added.

Much of China goes back to work on Monday, after the Lunar New Year holiday was extended in an attempt to rein in the virus. The fear now -- as tens of millions of people travel across the country and cities return to usual business -- is that new self-sustaining epidemic spots will rear up.

Many schools and universities across the country will remain closed for much of next week.

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Evacuation and spread

As Wuhan and much of Hubei remains on lockdown in a bid to contain the virus, many countries have begun extracting their citizens from the city.

A charter plane carrying more than 350 South Koreans landed at Gimpo International Airport near Seoul on Friday, following flights organized by the US and Japan to evacuate their citizens. Multiple other governments, including the UK, Australia, New Zealand and Canada are still arranging flights.

Meanwhile, more cases of the virus have been reported worldwide. Singapore confirmed three additional cases Thursday, bringing the total number of confirmed infections in the city to 13.

Health officials said all 13 cases are in a stable condition and "most are improving." They also advised citizens to "defer all travel to Hubei Province and all non-essential travel to mainland China."

The Singapore government said it will distribute four masks each to 1.3 million households in the city from Saturday. Other Asian territories, particularly Hong Kong, have struggled to maintain supply of masks, with many stores running out following an initial rush by residents to stock up.

More than 130 infections with the virus -- but no deaths -- have been reported outside mainland China.

The UK has confirmed its first two cases of Wuhan coronavirus in the northwest of England, according to a statement by Chris Whitty, the chief medical officer for England.

"We can confirm that two patients in England, who are members of the same family, have tested positive for coronavirus. The patients are receiving specialist NHS (National Health Service) care, and we are using tried and tested infection control procedures to prevent further spread of the virus," he said.

"The NHS is extremely well-prepared and used to managing infections and we are already working rapidly to identify any contacts the patients had, to prevent further spread," he added.

"We have been preparing for UK cases of novel coronavirus and we have robust infection control measures in place to respond immediately. We are continuing to work closely with the World Health Organization and the international community as the outbreak in China develops to ensure we are ready for all eventualities."

Two of China's neighbors have instituted emergency measures to try and stop the virus spreading there. Russia said it was closing its border in the Far East, and limiting rail services from all of China from January 31. Meanwhile, North Korea declared a state of emergency and said it was instituting a "hygienic and anti-epidemic" response.

Work continues on Wuhan Huoshenshan hospital on January 30, 2020 in Wuhan, China. The 1,000-bed hospital is scheduled to open on February 5.

Facing a long quarantine

Much of Hubei has been under effective quarantine for weeks now, with almost every city facing travel restrictions in a province home to nearly 60 million people. Wuhan has been completely locked down, with residents cooped up in their homes and the streets abandoned.

Foreigners being airlifted out of the city are also facing up to two weeks of mandatory or voluntary quarantine once they land in their home countries.

However, this has sparked controversy in some countries, especially in Australia, where a plan to house evacuees in a former detention center for migrants on Christmas Island has generated no small amount of negative publicity .

Public broadcaster ABC spoke to some Australians in Wuhan who said they would rather remain in the city than face two weeks on what has been described by some opposition lawmakers as a "leper camp," even as Canberra defended its decision as the only place capable of quarantining hundreds of people.

At March Air Reserve Base in Southern California, where US evacuees were flown earlier this week, one man said he was willing to remain under quarantine "as long as I need."

Jarred Evans said that the US Centers for Disease Control told evacuees that the initial 72-hour quarantine that was suggested "is really not enough time, but you know, they're not obligated to keep us here."

"You're not obligated to leave (when the 72 hours are up), so they're saying that the best thing for you, your people, your family and the community is to stay as long as possible," Evans said.

After flying out of near-freezing temperatures in Wuhan, Evans said he and the other passengers were spending time outdoors enjoying the sunny, 22 degrees Celsius (72F) weather.

"We're all still taking major precautions. So it's not like we're around here hugging each other and shaking hands and things like that," Evans said. "We're wearing our masks ... But honestly, you know, everyone is enjoying themselves because what we experienced, what we've seen, is very serious, you know, people are dying. So when you see that and think about things like that, try to take as much appreciation of what is in front of you."

What happens next?

Speaking on Friday, China's Foreign Ministry said the country had full "confidence and capability" in winning the fight against the virus.

"Since the outbreak of the novel coronavirus epidemic, the Chinese government has been taking the most comprehensive and rigorous prevention and control measures with a high sense of responsibility for people's health," said ministry spokeswoman Hua Chunying in a statement. "Many of these measures go well beyond the requirements of the International Health Regulations. We have full confidence and capability to win this fight against the epidemic."

China has taken major measures to try and contain the epidemic, locking much of Hubei down, partially closing the border with Hong Kong and extending the Lunar New Year holiday, all of which could have a severe drain on the country's economy, already vulnerable due to the US-China trade war.

With most people due to go back to work on Monday, it remains unclear whether more measures will be announced, and if not, how this will influence the spread of the virus.

Health experts previously estimated that the number of cases could be far higher than currently confirmed. Researchers at Imperial College London have estimated that at least 4,000 people were infected in Wuhan by January 18, almost a week before the lockdown began. Their model suggests a low national figure of 20,000 infections by the end of the month, potentially as high as 100,000.

Researchers in Hong Kong estimate there could be 75,815 people in Wuhan infected with coronavirus as of January 25, according to a paper published Friday in The Lancet.

UPDATE: This story has been updated to reflect the number of confirmed cases of Wuhan coronavirus outside mainland China.