Friday's cyber-attack has affected more than 200,000 victims in 150 countries, Europol chief Rob Wainwright says.
Speaking to Britain's ITV, he said the world faced an escalating threat, and there was concern about the level of potential attacks 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 he was concerned that the numbers of those affected would continue to rise when people returned to work on Monday morning.
"We're in the face of an escalating threat, the numbers are going up," he said, adding that the current attack was unprecedented.