Friday’s cyber-attack has affected more than 200,000 victims in 150 countries, Europol chief Rob Wainwright says.
He told the BBC the act was “unprecedented in its scale” and warned more people could find themselves affected on Monday morning.
The virus took control of users’ files, demanding payments; Russia and the UK were among the worst-hit countries.
Experts say another attack could be imminent and have warned people to ensure their security is up to date.
Mr Wainwright said that the ransomware was being combined with a worm application allowing the “infection of one computer to quickly spread across the networks”.
He added: “That’s why we’re seeing these numbers increasing all the time.”
‘Patch before Monday’
Although a temporary fix earlier slowed the infection rate, the attackers had now released a new version of the ransomware, he said.
Companies need to make sure they have updated their systems and “patched where they should” before staff arrived for work on Monday morning, the EU law enforcement agency head said.
In England, 48 National Health Service (NHS) trusts reported problems at hospitals, GP surgeries or pharmacies, and 13 NHS organisations in Scotland were also affected.
What occurred was an “indiscriminate attack across the world on multiple industries and services”, Mr Wainwright said, including Germany’s rail network Deutsche Bahn, Spanish telecommunications operator Telefonica, US logistics giant FedEx and Russia’s interior ministry.
However, he said that so far “remarkably” few payments had been made by victims of the attack.
BBC analysis of three accounts linked with the global attack suggests the hackers have been paid the equivalent of £22,080.