Europol executive director Rob Wainwright said the situation could worsen on Monday when workers return to their offices after the weekend and log on.
The NHS says it employs more than 1.5 million people, making it one of the world's largest employers alongside the US Department of Defense, Walmart and the Chinese army.
GP practices in the North East of England, which were impacted by Friday's cyber-attack on the NHS, are now able to use their IT systems again.
I am anxious about how the numbers will continue to grow when people go to work and turn on their machines on Monday morning.
In Australia, Alistair MacGibbon, special advisor to Prime Minister Malcolm Turnbull on Cyber Security, said some small businesses would likely be hit "but as a whole of nation we can be confident, so far, that we have missed the worst of this".
The Leatside Surgery was hit in on Friday afternoon after NHS computer systems across the country were hit by a ransomware attack.
More than 200 000 victims in 150 countries and regions were afflicted by the attacks with Russian Federation and the United Kingdom the worst hit.
On Sunday night, Microsoft blamed the United States spy agency that had originally developed software that allowed the ransomware attack to infect computers.
Kent Community Health Trust, which runs community hospitals and minor injuries units across the county, was not a victim of the attack, but reportedly shut down its digital servers as a precautionary measure - causing disruption despite not being affected directly.
The ransomware virus locked files and demanded payment to allow access and avoid data being destroyed.
The virus exploits a vulnerability in Microsoft Windows software, first identified by the US National Security Agency, experts have said.
"We're obviously working with that business, the Australian Cyber Security Centre is engaging with them".
The Health Secretary Jeremy Hunt was warned about the failure to update cyber security on NHS IT systems a year ago.
What is the WannaCry virus?