Wainwright said he was anxious that the ransomware attack might spread further once people return to work on Monday and log on to their computers.
"The software has actually stopped spreading across the world", he told CNN.
It turned out that the ransomware code was written to connect to an unregistered domain and "if the connection is not successful it ransoms the system, if it is successful, the malware exits".
A global cyber attack forced a European carmaker to halt some production lines, hit Russian computers with more than half of suspected infections, struck schools in China and hospitals in Indonesia, though it appeared to be dying down on Saturday.
England's largest partnership of rural service providers - has voiced concern at the impact of cyber-attacks on doctors' surgeries that serve rural communities. "Yet still the senior people stick with the old anti-virus technology that simply doesn't work and in the process, they're putting organisations like the NHS at risk". Staff were reportedly told to turn off their computers.
So how can people and organizations protect themselves against such attacks? But U.K. hospitals, Chinese universities and global firms like Fedex also reported they had come under assault.
But Europol head Rob Wainwright said he was concerned that the number affected would continue to rise when people returned to work on Monday morning.
Some of the biggest disruption was caused by attacks on the United Kingdom health system, which saw hospitals and clinics forced to turn away patients after losing access to computers.
The virus exploits a vulnerability in Microsoft Windows software, first identified by the US National Security Agency, experts have said.
It combined a known and highly risky security hole in Microsoft Windows, tardy users who didn't apply Microsoft's March software fix, and a software design that allowed the malware to spread quickly once inside university, business and government networks.
State agencies and major companies around the world were left reeling by the attacks which blocked access to files and demanded ransom money, forcing them to shut down their computer systems.
"We are aware some bodies, which range from practices to trusts, may have suspended selected systems purely as a precautionary measure", a spokesman said.
Russia's Interior Ministry acknowledged a ransomware attack on its computers.
Who perpetrated this wave of attacks remains unknown.
In Britain, which is in the middle of an election campaign, the cyberattack triggered criticism of the the National Health Service's aging computer systems, particularly the use of Windows XP, an outdated version of the Microsoft operating system that doesn't have the same level of defense against cyberattacks as newer operating systems.
Do not open any attachment unless you expect to receive this file, the malware could exploit the sender's email (even from someone you know).
The virus also has a wormlike features that looks for other vulnerable systems once it's embedded in your computer, which means it can spread to other computers in a network.
Home Secretary Amber Rudd will chair a meeting of the Government's emergency COBRA committee later.
"There are also a small number of reports made to the Australian Cybercrime Online Reporting Network that may be cases of this ransomware campaign, but these have yet to be confirmed", said MacGibbon.