The attack has hit more than 75,000 computers in 99 countries.
Experts have warned the number of victims "will continue to grow" as people return to work on Monday.
The Japan Computer Emergency Response Team Coordination Center, a nonprofit providing support for computer attacks, said 2,000 computers at 600 locations in Japan were reported affected so far.
"We're in the face of an escalating threat, the numbers are going up".
The indiscriminate attack, which began Friday, struck banks, hospitals and government agencies, exploiting known vulnerabilities in old Microsoft computer operating systems.Europol executive director Rob Wainwright said the situation could worsen today when workers return to their offices after the weekend and log on.
But Mr MacGibbon said the ransomware could be adapted by the criminals and was not willing to say the threat of compromise was over. "That's not to say that the attacks are new - it's a repercussion of what happened on Friday".
He said: "We have been concerned for some time that the healthcare sectors in many countries are particularly vulnerable".
And there is the possibility of more to come, according to Assistant Minister for cyber-security, Dan Tehan.
'We're not talking about a government organisation or a hospital or anything like that.
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Nissan Motor Co. confirmed Monday some units had been targeted, but there was no major impact on its business.
Companies need to make sure they have updated their systems and "patched where they should" before staff arrived for work on Monday morning, the European Union law enforcement agency head said.
"They're aware of this".
Professor Helen Stokes-Lampard of the Royal College of General Practitioners said many Global Positioning System went into their practices on Sunday to reboot their computers and install updates.
"We have seen vulnerabilities stored by the CIA show up on WikiLeaks, and now this vulnerability stolen from the United States military intelligence organisation National Security Agency (NSA) has affected customers around the world", Smith wrote.
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.
High-profile victims include hospitals in Britain, the Spanish telecoms giant Telefonica, French carmaker Renault, US package delivery company FedEx, Russia's interior ministry and the German rail operator Deutsche Bahn.
The identity of the hacker who perpetrated the wave of attacks remains unknown. Security agencies in affected countries were racing to find out.
"Version 1 of WannaCrypt was stoppable but version 2.0 will likely remove the flaw. You're only safe if you patch as soon as possible", he tweeted.