US President Donald Trump has played down fears of a major coronavirus outbreak in the US, even as infections ricochet around the world, prompting a ban on pilgrims to Saudi Arabia.

China is no longer the only breeding ground for the deadly virus as countries fret over the possible contagion coming from other hotbeds of infection, including Iran, South Korea and Italy.

There are now more daily cases being recorded outside China than inside the country, where the virus first emerged in December, according to the World Health Organisation (WHO).

More than 2,700 people have died in China and some 78,500 have been infected. There have been more than 65 deaths and 3,600 cases in dozens of other countries.

“We really think we’ve done a great job in keeping it down to a minimum. We’ve had tremendous success, beyond what people would’ve thought,” Trump told reporters at the White House.

His comments contradicted US health officials who urged Americans to be ready to cancel mass gatherings and work from home. There are 60 cases in the US so far.

Following Trump’s upbeat assessment, the US Centres for Disease Control and Prevention said it had detected the first case of unknown origin in the country, signalling that the virus may be spreading within communities.

The US and other countries are also bracing for more cases to be imported from abroad.

Several governments have advised against travel to Italy – which has 470 cases and 12 deaths. Iran’s neighbours have shut their borders, while Mongolia has suspended flights from South Korea and Japan.

Trump said his country was considering travel restrictions on Italy and South Korea, which has almost 1,600 cases, the highest number outside China. The US already restricts arrivals from China.

Even China – which quarantined an entire province and shut down cities across the country to contain the virus – is now worried about importing cases as it mulls its own travel restrictions.

Beijing has ordered people arriving in the capital from countries hit by the virus to go into 14-day self-quarantine.

The virus is believed to have originated in a market in the central Chinese city of Wuhan, where it hopped from an animal to a human before spreading across the country and proliferating abroad.

China reported 32 more deaths Thursday – its lowest daily tally since January – and 435 new cases, most of them in hard-hit Hubei province and well below massive increases from just a week ago.

But other countries have become sources of concern.

The Brazilian Ministry of Health confirmed Latin America’s first case – a Brazilian 61-year-old man who had travelled to Italy’s Lombardy region.

In Romania, a man was infected after coming in contact with an Italian who visited the country.

Greece’s first case is a woman who had been in northern Italy, while France, Spain, Croatia, Austria, North Macedonia and Algeria have all reported cases linked to Italy.

A man who returned from a skiing holiday in northern Italy became Denmark’s first case.

With the virus spreading in the Middle East, Saudi Arabia suspended visas for visits to Islam’s holiest sites for the “umrah” pilgrimage, an unprecedented move triggered by coronavirus fears that raise questions over the hajj, which starts in July.

The Ministry of Foreign Affairs said it was also suspending visas for tourists visiting from countries where the new virus is a “danger”.

Iran has emerged as a major hotspot in the region, where 19 people have succumbed to the disease – the biggest death toll outside of China.

The Islamic Republic imposed domestic travel restrictions for people with confirmed or suspected cases and slapped curbs on visits to major Muslim pilgrimage sites, but it said it was not quarantining cities.

The US and South Korea’s militaries on Thursday postponed forthcoming joint exercises due to the outbreak.

Fears over the epidemic’s spread have rocked global markets in recent days, while sports matches and festivals across Europe have been cancelled.

The WHO has urged countries to prepare for a potential pandemic, though it stopped short of declaring one.

It has warned that poor countries are particularly at risk, sparking fears of how countries in Latin America and Africa would cope.

A Six Nations rugby match between Italy and Ireland in Dublin on March 7 has been called off, and the alpine skiing World Cup Finals – due to take place in Italy next month – will be held without any fans on the slopes.

However, EU Health Commissioner Stella Kyriakides appealed for calm.

“This is a situation of concern, but we must not give in to panic,” Kyriakides told reporters in Rome.