It's on track to be one of the biggest recorded ransomware attacks ever, with tens of thousands of infected computers in almost 100 countries.
It has crippled Britain's health system - with stroke victims unable to undergo urgent surgery because their scans could not be accessed - and affected other businesses around the world.
The Europol chief said his agency 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 ransomware, called WannaCry, locks down files on an infected computer and asks the computer's administrator to pay in order to regain control of them.
A number of popular websites like Amazon and Netflix were down for some users on Friday morning in what appears to be a massive DDoS attack.
Europol Director Rob Wainwright told ITV's Peston on Sunday programme the attack was unique in that the ransomware was used in combination with "a worm functionality" so the infection spread automatically.
In an interview on ABC's "This Week", Clapper said the worry was "this ransomware attack will be even larger" as people return to their desks after the weekend.
In a blog post Friday night, Microsoft also said it had produced a "signature" that allows its Windows Defender antivirus engine to provide "defense-in-depth" protection.
WannaCrypt exploits a Windows vulnerability patched in March by Microsoft.
Computers around the globe were hacked beginning on Friday using a security flaw in Microsoft's Windows XP operating system, an older version that was no longer given mainstream tech support by the USA giant.
A British cyber whiz was hailed an "accidental hero" after he registered a domain name that unexpectedly stopped the spread of the virus, which exploits a vulnerability in Microsoft Windows software.
The attack held users hostage by freezing their computers, encrypting their data and demanding money through online bitcoin payment - $300 at first, rising to $600 before it destroys files hours later.
Another government security official said no government systems were affected.
An anonymous malware researcher inadvertently helped stop the spread of a global cyberattack that targeted almost 100 countries.
F-Secure's chief research officer Mikko Hypponen said Russian Federation and India were particularly hard-hit because many there were still using Windows XP.
In another development, an Indian-origin NHS doctor Krishna Chinthapalli said he had warned against the cyber-hack of the National Health Service (NHS) just two days before it corrupted and crippled the network. Around a fifth of trusts were hit amid concerns networks were left vulnerable because they were still using outdated Windows XP software.
Experts said the spread of the virus, dubbed WannaCry, which locked up more than 200,000 computers - had slowed, but the respite might only be brief.
You can try a decryption tool to unlock your data, but that won't always work, and hackers will sometimes use such apps as bait to further infect your system (so if you download one, only get it from a trusted, official site).
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