Europol has also warned a "complex international investigation" was required "to identify the culprits".
It's emerged that the tools used in the attack appear to have been stolen from the US National Security Agency.
There have been reports of infections in as many as 100 countries, including several in New Zealand, a live-tracking map of the attack showed.
European countries, including Russia, were among the worst hit.
Although the spread of the malware - known as WannaCry and variants of that name - appears to have slowed, the threat is not yet over.
Europol said its cyber-crime team, EC3, was working closely with affected countries to "mitigate the threat and assist victims".
In the UK, a total of 48 National Health trusts were hit by the cyber-attack, of which all but six are now back to normal, according to the Home Secretary Amber Rudd.
The attack left hospitals and doctors unable to access patient data, and led to the cancellation of operations and medical appointments.
Some reports say Russia has seen more infections than any other country.
Banks, the state-owned railways and a mobile phone network were hit.
Russia's interior ministry said 1000 of its computers had been infected but the virus was swiftly dealt with and no sensitive data was compromised.
In Germany, the federal railway operator said electronic boards had been disrupted.
France's carmaker Renault was forced to stop production at a number of sites.
Meanwhile, the New Zealand government's cyber emergency response team (CERT) is looking into the attack.