The World Health Organization warned that sustained transmission of monkeypox could cause the disease to move into high risk groups, such as pregnant women, immunocompromised people and children.
The WHO said it was investigating reports of infected children, including two cases in Britain, as well as following up reports in Spain and France.
None of the cases in children have been severe.
The virus has been identified in more than 50 countries outside of the African nations where it has been endemic.
The WHO is calling for testing to be ramped up, as cases in those countries are rising.
I'm concerned about sustained transmission because it would suggest that the virus is establishing itself and could move into high risk groups like children, the immunocompromised and pregnant women, WHO chief Tedros Adhanom Ghebreyesus said.
Since the outbreak began in May, there have been more than 3,400 cases of monkeypox, and one death, mainly in Europe among men who have sex with men, according to a WHO tally.
There have been more than 1,500 cases and 66 deaths in countries this year where it is more commonly spread.
Last week, the WHO ruled that the outbreak did not represent a public health emergency, its highest level of alert.
The WHO's emergency programme executive director Mike Ryan said that the WHO was closely monitoring the outbreak and would reconvene the committee as soon as possible to assess whether this was still the case.
He said that WHO was working on a mechanism to distribute vaccines more equitably after countries like Britain and the US suggested they were willing to share their stockpiled smallpox vaccines, which also protects against monkeypox.