The World Health Organization (WHO) said that 780 laboratory-confirmed monkeypox cases had been reported from 27 countries, while maintaining that the global risk level was moderate.
The WHO said the figure, which totals cases from 13 May to 2 June was probably an underestimate due to limited epidemiological and laboratory information.
"It is highly likely that other countries will identify cases and there will be further spread of the virus," the UN health agency added.
Few hospitalisations have been reported, apart from patients being isolated.
The WHO listed the countries reporting the most cases as: Britain (207), Spain (156), Portugal (138), Canada (58) and Germany (57).
Six cases of monkeypox have now been confirmed in Ireland.
Besides Europe and North America, cases have also been reported in single figures in Argentina, Australia, Morocco and the United Arab Emirates.
One case of monkeypox in a non-endemic country is considered an outbreak.
"Some countries are reporting that new generations of cases are no longer appearing only among known contacts of previously confirmed cases, suggesting that chains of transmission are being missed through undetected circulation of the virus," the WHO said.
"The public health risk could become high if this virus exploits the opportunity to establish itself in non-endemic countries as a widespread human pathogen.
"WHO assesses the risk at the global level as moderate considering this is the first time that many monkeypox cases and clusters are reported concurrently in non-endemic and endemic countries."
Many cases were not presenting with the classical clinical picture for monkeypox: some have described having pustules (large pimple) appear before symptoms such as fever, and having lesions at different stages of development, both of which have been described as atypical.
Most of the reported cases so far have been presented through sexual health or other health services, and have mainly involved men who have sex with men, the WHO said.
The WHO said there had been no deaths associated with outbreaks in non-endemic countries, but cases and deaths continue to be reported from endemic areas.
Dr @mvankerkhove explains 5⃣ key actions to prevent #monkeypox 👇 pic.twitter.com/IbO11jvgtx
— World Health Organization (WHO) (@WHO) June 4, 2022
The WHO listed the endemic states as Cameroon, the Central African Republic, Congo-Brazzaville, the Democratic Republic of the Congo, Liberia, Nigeria, Sierra Leone, Gabon and Ivory Coast, plus Ghana where it has been identified in animals only.
Last week the WHO convened virtually more than 500 experts and over 2,000 participants to discuss monkeypox knowledge gaps and research priorities.
Experts stressed the need for clinical studies of vaccines and treatments to better understand their effectiveness, and called for faster research into the disease epidemiology and transmission.