The virus took control of users' files, demanding payments; Russian Federation and the United Kingdom were among the worst-hit countries.
It was not yet known who perpetrated Friday's attacks. "We've seen that the slowdown of the infection rate over Friday night, after a temporary fix around it, has now been overcome by a second variation the criminals have released".
But the agency added that some infections may not yet have been detected, and that existing infections can spread within networks.
Dr Krishna Chinthapalli said the havoc wreaked on some health services in an worldwide cyber attack could encourage hackers to target hospitals. The James Paget University Hospital in Gorleston was among those affected. "It's a big priority of mine that we protect the financial infrastructure", he said.
That was the chilling prediction made yesterday by Ron Wainwright, the English-born head of the EU's crimefighting organisation Europol.
Prime Minister Malcolm Turnbull has urged Australians to update their Windows operating systems in the wake of a global cyber attack.
Few banks in Europe were affected after learning from previous experiences of attacks, Mr Wainwright said but an attack on public health systems, which badly affected the NHS, had caused concern.
The Computer Emergency Response Team of Turkey tweeted that the "wannacry ransomware" is spread over Server Message Block flaws.
Microsoft patched the "hole" in the newest versions of its operating software - Windows 10 for most home users - in March, three weeks before the stolen NSA exploit software was published on the internet.
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Experts said it appeared that the ransomware had made just over $32,000, although they expected that number to pop when people went back into the office Monday.
By one security firm's count, the malware struck at least 74 countries, including the USA, where its effects seemed muted. Investigators are working to track down those responsible for the ransomware used on Friday, known as Wanna Decryptor or WannaCry.
The Garda had said early on Sunday there was no identified cyber attack on any Irish State computer system from the wave of global ransomware attacks.
That said, some people often pay the cash just to retrieve important files.
Britain's state-run National Health Service was affected by the attack.
"You can't force businesses to patch critical Windows vulnerabilities", said Adrian Sanabria, founder of security firm Savage Security.
In contrast to reports from several European security firms, a researcher at the Tripwire company on the U.S. West Coast said late Saturday that the attack could be diminishing. "This attack provides yet another example of why the stockpiling of vulnerabilities by governments is such a problem".
Russia's Interior Ministry acknowledged a ransomware attack on its computers. In 2016, Hollywood Presbyterian Medical Center in California said it had paid a $17,000 ransom to regain control of its computers from hackers. As an additional "defense-in-depth" measure, keep up-to-date anti-malware software installed on your machines. Here's how to turn automatic updates on.
It comes amid warnings that the crisis could spread to other sectors, with a wider "escalating threat" as millions of workers switch on their computers.