In France, two confirmed cases of the new SARS-like virus were recorded at the weekend.
The World Health Organisation called on people to stay calm and not overburden hospitals for fear of the deadly virus to allow for proper treatment of those actually infected.
"We need the health system to be able to take care of those (infected) patients and people who legitimately have this disease... We do not want to overburden the health system," WHO spokesman Gregory Hartl told AFP.
"There have only been less than a handful of cases in France so far... The chances are very small that anyone in France has this disease."
The coronavirus, known as nCoV-EMC, is a cousin of the virus that causes Severe Acute Respiratory Syndrome (SARS), which killed nearly 800 people in the Far East in 2002-03.
In all, 34 cases have been reported worldwide since the virus was first detected in September 2012, with 18 of the victims dying, mostly in Saudi Arabia.
While the virus has been deadliest in Saudi Arabia, cases have also been reported in Jordan, Germany, Britain and France.
Hartl said the WHO currently sees no reason to change its travel recommendations because of the new virus.
"We have not seen general transmission in the community, again we have only seen transmission among very, very close contacts," he said. "So from that point of view the risk is very small and there is no reason yet to make any changes to our recommendations".