The latest new cases were reported in France, Italy and Sweden.
It follows the confirmation of cases in the US, Spain and Portugal on Wednesday, as well as the investigation of 13 suspected cases in Canada.
Monkeypox is most common in remote parts of Central and West Africa.
Cases of the disease outside of the region are often linked to travel to the area.
Monkeypox is a rare viral infection which is usually mild and from which most people recover in a few weeks, according to the UK's National Health Service.
The virus does not spread easily between people and the risk to the wider public is said to be very low.