Most infections are in China but other countries including South Korea, Italy and Iran are battling to contain the virus, which causes the respiratory disease Covid-19.
A pandemic is declared when an infectious disease threatens different parts of the world simultaneously.
No vaccine is available so far to prevent the new coronavirus.
About 77,000 people in China, where the virus emerged last year, have been infected and nearly 2,600 have died.
More than 1,200 cases have been confirmed in 26 other countries and there have been eight deaths, the World Health Organization (WHO) says.
On Monday Afghanistan, Kuwait and Bahrain reported their first cases, all involving people who had returned from Iran.
WHO chief Tedros Adhanom Ghebreyesus had warned that the window of opportunity to contain the virus was “narrowing”.
Paul Hunter, professor of health protection at the University of East Anglia in the UK, echoed his fears, saying the spike in cases outside China was “extremely concerning”.
“The tipping point after which our ability to prevent a global pandemic seems a lot closer after the past 24 hours,” he said on Monday.
World edges closer to coronavirus pandemicAnalysis by Fergus Walsh, medical correspondent
The combined situation in South Korea, Iran and Italy points to the early stages of pandemic. This means a global outbreak, with the coronavirus spreading in the community in multiple parts of the world.
In each of these countries we are seeing spread of the virus with no connection to China. The lockdown efforts in Italy mirror those that have happened in China.
The situation in Iran is especially worrying, because the health authorities have reportedly said the virus has spread to multiple cities, and it appears the first case in Lebanon is linked to a traveller from Iran.
If we have a pandemic, it will still be important to limit the speed of spread of the virus.
If countries could hold it somewhat at bay until the end of winter, there is a hope that warmer temperatures will reduce the time the virus can survive in the air, as we see with seasonal flu. But this may not be certain.