The threat from the cyber attack that crippled worldwide services "will continue to grow" as people return to work on Monday, the head of Europol warned.
The attack is a virus that locks people out of their computer files until they pay a ransom to the hackers.
Lawrence Abrams of BleepingComputer.com in NY says many organizations don't install security upgrades because they're anxious about triggering bugs, or they can't afford the downtime.
"It's an global attack and a number of countries and organisations have been affected", British Prime Minister Theresa May said.
And to be safe from other similar kinds of attacks users should always use a trustworthy antivirus software and a firewall, backup files in a separate system and set a popup blocker.
But the agency added that some infections may not yet have been detected, and that existing infections can spread within networks.
At least three local organisations have been hit by WannaCrypt/WannaCry, according to the Australian government.
The attack therefore spread faster than previous, smaller-scale ransomware attacks.
"At the moment, we are in the face of an escalating threat", he told the British network ITV Sunday.
Europol's Wainwright underscored the point Sunday.
Microsoft released patches last month and on Friday to fix a vulnerability that allowed the worm to spread across networks.
In the U.S., FedEx reported that its Windows computers were "experiencing interference" from malware, but wouldn't say if it had been hit by ransomware.
Microsoft said it had released a Windows security update in March to tackle the problem involved in the latest attack, but many users were yet to run it.
Krishna Chinthapalli, a doctor at Britain's National Hospital for Neurology & Neurosurgery who wrote a paper on cybersecurity for the British Medical Journal, warned that British hospitals' old operating systems and confidential patient information made them an ideal target for blackmailers.
He said Russian Federation and India were hit particularly hard, largely because Microsoft's Windows XP - one of the operating systems most at risk - was still widely used there. "I am anxious about how the numbers will continue to grow when people go to work and turn their machines on Monday morning". Use a reputable security software to prevent attacks in the future.
"I think 20, 30 thousand dollars' worth of dollars only", Wainwright said.
WannaCry has already caused massive disruption around the globe.
In England, 48 National Health Service (NHS) trusts fell victim, as did 13 NHS bodies in Scotland.
Microsoft said the situation was "painful" and that it was taking "all possible actions to protect our customers".
In China, the internet security company Qihoo360 issued a "red alert" saying that a large number of colleges and students in the country had been affected by the ransomware, which is also referred to as WannaCrypt.
Users of the old Windows XP system can find the ransomware patch for that system here.
Spain's Telefonica, a global broadband and telecommunications company, was among the companies hit. More than 200,000 computers have been affected so far. A top Russian mobile operator said Friday it had come under cyberattacks that appeared similar to those that have crippled some United Kingdom ho.
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.