The World Health Organisation's (WHO) Director-General, Tedros Adhanom Ghebreyesus, said the organisation would not describe Covid-19 as a pandemic at present - but admitted it could change.
"Does this virus have pandemic potential? Absolutely it has. Are we there yet? From our assessment, not yet," he said.
"Now is not the time to focus on what word we use. That will not prevent a single infection today."
Cases have doubled in Italy within a matter of days, forcing neighbouring countries to clamp down on travel to and from affected parts.
North Korea meanwhile has quarantined hundreds of foreigners and the South has increased its anti-virus alert to the highest level.
In Iran, a politician has said 50 people have died in the city of Qom.
ITV News Science Editor Tom Clarke explains why the WHO is treading so carefully with China
The WHO is currently describing the virus as an "epidemic" with "clusters and outbreaks in some countries."
Close to 80,000 cases have been reported worldwide, with 2,600 deaths.
Spokeswoman Margaret Harris said in most cases there was a clear link between those affected and cases first reported in Asia.
"If it became clear that it is all around the globe and we are seeing systematic community transmission, then we would say this meets the definition of a pandemic," she said.
How the virus is spreading across the world
Here's how various countries around the world are reacting to the spread of Covid-19:
North Korea has quarantined around 380 foreigners in a bid to stop an the outbreak, while cases in Italy have doubled in just a few days to more than 160.
It is believed those who have been quarantined in Pyongyang are diplomats stationed in the capital, and those involved in overseas trading.
North Korea has not reported any cases of Covid-19 since the respiratory disease was first identified in Wuhan, but it has taken various preventative measures including strengthening its border with China and doubling the quarantine period to 30 days against those coming from foreign countries.
The country is bordered by China - which has borne the brunt of the illness with more than 2,600 deaths and more than 77,000 cases - and South Korea, which is the second-worst hit country after China, with seven deaths and 833 cases.
Downing Street insisted on Monday the UK remains "prepared for all eventualities", a among the 32 Diamond Princess passengers who were flown back from a two-week quarantine aboard the coronavirus-hit cruise ship docked in Japan.
There have been 13 confirmed cases of coronavirus in the UK.
All those on board the ship - where almost one-fifth of the 3,711 passengers originally on board contracted the virus and three have died - had tested negative for the illness before being allowed to board the plane.
The remaining 28 remain in quarantine at Arrowe Park Hospital on The Wirral.
"We are well prepared for UK cases, we are using tried and tested procedures to prevent further spread and the NHS is extremely well-prepared and used to managing infections," the Prime Minister's spokesperson said.
Some British passengers opted to stay on board the ship and four Britons who tested positive for coronavirus are being treated in hospital in Japan, including David and Sally Abel who documented their isolation and
Concern was also on the rise in Austria, which halted all rail traffic to and from Italy for several hours after suspicion that a train at its southern border with Italy had two passengers possibly infected with the virus on board, authorities said.
Austria's interior ministry said it had been informed by Italy's railway company that two passengers had a fever and stopped the train at the Brenner crossing before it could enter Austria.
However, just before midnight Austria's Federal Railways announced on Twitter the ban had been lifted.
Austrian Interior Minister Karl Nehammer said the two people suspected of being infected with the virus on the Eurocity 86 train from Venice to Munich had tested negative and the train would be allowed to continue on its way, according to the ORF broadcast network.
China and Iran
There are fears that a coronavirus outbreak in North Korea could be particularly devastating, as the country lacks key medical supplies and infrastructure to test and treat infected people.
In neighbouring China, there were 150 more Covid-19 deaths overnight, the largest rise in more than a week.
ITV News Asia Correspondent Debi Edward reports China has postponed its annual Parliament meeting in Beijing, which was due to take place in March.
In Iran, semiofficial ILNA news agency is reporting the death toll from the virus in the city of Qom is 50 - despite the Health Ministry insisting 12 deaths have been recorded to date.
An official from Qom, Ahmad Amiriabadi Farahani, was quoted in ILNA saying that more than 250 people are in quarantined in the city, which is a popular place of religious study for Shiites from across Iran and other countries.
He said the 50 deaths date as far back as February 13. Iran, however, first officially reported cases of the virus and its first deaths on February 19
Meanwhile in South Korea, although officials have expressed hope they could contain the outbreak to the region surrounding Daegu, some experts noted signs of the virus circulating nationwide, including a number of cases in the capital Seoul.
However, more than 140 of the country's new cases were in and near the city of Daegu, where most of the country's infections have occurred so far.
South Korean President Moon Jae-in said his government had increased its anti-virus alert level by one notch to "red," the highest level.
It allows for the temporary closure of schools and reduced operation of public transportation and flights to and from South Korea.
The new school year in South Korea was postponed by one week until March 9.
Mr Moon said the outbreak "has reached a crucial watershed," and that the next few days will be critical.
"We shouldn't be bound by regulations and hesitate to take unprecedented, powerful measures," he added
Elsewhere, authorities in Italy have battled to contain Europe's first major outbreak and Iran reported eight deaths - the highest toll outside of China.
Some of the disease clusters identified in recent days have shown no link to China, a worrying sign of the virus spreading beyond control.
In Italy's northern Lombardy region, which includes the nation's financial capital Milan, the governor announced the number of confirmed cases stood at 110.
Italy now has the largest number of cases outside Asia with 152 cases and three deaths with the most recent on Sunday.
Streets in Italy are all but deserted as 12 towns were put in lockdown