"Based on the current situation and available information, WHO encourages all Member States to continue their surveillance for severe acute respiratory infections (SARI) and to carefully review any unusual patterns," the United Nations health agency said in a statement.
On Friday, British health authorities said that a third member of a family had been diagnosed with so-called novel coronavirus, but was not in danger.
"Although this new case offers further indications of person-to-person transmission, no sustained person-to-person transmission has been identified," said the WHO.
"Testing for the new coronavirus should be considered in patients with unexplained pneumonias, or in patients with unexplained severe, progressive or complicated respiratory illness not responding to treatment," it added.
Clusters of cases, and cases among health workers, should be thoroughly investigated wherever they occur, it underlined.
Britain's Health Protection Agency said the latest person to contract the virus was a relative of two other cases announced earlier this week.
The first member of the family, who was confirmed on Monday as having the virus, had recently travelled to the Middle East and Pakistan. The two relatives had no recent travel history.
A total of 12 cases have been reported to the WHO, with five of them fatal -- three in Saudi Arabia and two in Jordan.
Coronaviruses are to blame for most common colds but can also cause SARS (severe acute respiratory syndrome).
A SARS epidemic killed more than 800 people when it swept out of China in 2003, sparking a major international health scare.