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.
"We are running around 200 global operations against cyber crime each year but we've never seen anything like this.
"The latest count is over 200,000 victims in at least 150 countries. Many of those victims will be businesses, including large corporations. The global reach is unprecedented."
Analysis: How it started
He said the ransomware was unique because it was used in combination with a worm - allowing it to spread through an infected computer through an entire network.
However, Mr Wainwright 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.
The Europol chief said it was working with the US Federal Bureau of Investigation to find those responsible, and that more than one person was likely to be involved.
The virus exploits a vulnerability in Microsoft Windows software, first identified by the US National Security Agency, experts have said.
After taking computers over, it displayed messages demanding a payment of $300 (£230) in virtual currency Bitcoin to unlock files and return them to the user.
The UK security researcher known as "MalwareTech", who helped to limit the ransomware attack, predicted "another one coming... quite likely on Monday".
MalwareTech, who wants to remain anonymous, was hailed as an "accidental hero" after registering a domain name to track the spread of the virus, which actually ended up halting it.
The 22-year-old told the BBC it was very important for people to patch their systems as soon as possible.

Thank God they are not here yet.