The current form of MERS virus appears less infectious than originally thought, but the Asian countries have been advised to keep their guard against the deadly disease by a World Health Organization expert on Thursday.
The Middle East respiratory syndrome (MERS) has already killed 287 people, said Mark Jacobs, WHO's director for communicable diseases in the Western Pacific.
However the relatives of those infected have not been showing any signs of catching it, he added.
His comments come after the Philippines last week urged its large Muslim minority to reconsider plans to join the annual Hajj pilgrimage, which takes place in Saudi Arabia, until the threat from the virus has dissipated.
"A spread in our part of the world is small," Jacobs told reporters. "If the virus stays unchanged, then I think that what we have been seeing is what we will keep seeing."
Later Thursday, the WHO emphasized in a statement that the risk to Asian countries remained small only if the virus remained in its current form.
"Given that it is still not known how MERS spreads to people, WHO cannot predict how the virus will spread," the statement read. "Therefore, it is important that health authorities stay vigilant."
"Our understanding of the virus and the disease it causes is continuing to evolve," the statement continued, calling on all countries to "continue their surveillance for acute respiratory infections".
The WHO said 15 countries have reported MERS cases, with the virus widely circulating in the Arabian peninsula.
Outside the Middle East, both the Philippines and neighbor Malaysia have reported cases of patients who apparently caught the virus after travelling there.
These people had not infected others in their countries, according to a WHO report.
"We haven't seen big outbreaks in a community or anything like that to suggest that it's easy for some in the general community to be infected, (but) obviously we are keeping a close eye on that and hope that would not be the case," Jacobs said.
While there was always a chance of the virus spreading in health care facilities treating infected patients, "the risk to almost everyone in the world is extremely low".
Jacobs advised Asians travelling to Saudi Arabia for the Hajj in October to take precautions, including proper hygiene and staying away from people exhibiting symptoms like coughing.
The WHO has not issued any travel or trade restrictions or entry screening related to MERS.