"That's why we're seeing these numbers increasing all the time", he said.
He said most people "are living an online life", and these agencies have a duty to protect their countries' citizens in that realm as well.
New versions of the worm are expected, they said, and the extent of the damage from Friday's attack remains unclear.
A 22-year-old security researcher in the U.K, who goes by MalwareTech, registered that domain to analyze the attack, but it turned out the ransomware needed it to remain unregistered to keep spreading.
In England, 48 National Health Service (NHS) trusts fell victim, as did 13 NHS bodies in Scotland.
The companies and government agencies targeted were diverse.
More than 120 public bodies will be contacted to ensure their defences are adequate.
Investigators from around the globe, including the National Crime Agency (NCA), are working non-stop to hunt down those responsible for the Wanna Decryptor ransomware, also known as WannaCry.
Pyotr Lidov, a spokesman for Megafon, said Friday's attacks froze computers in company's offices across Russian Federation.
Ministers are to convene an extraordinary meeting of the National Cyber Resilience leaders' board on Tuesday to review the response to the breach.
"I think we need to keep a much closer eye on what government agencies are doing with these cyber weapons. because they could've tipped off the government, they could have tipped off users of these operating systems but they didn't, they kept those exploits to themselves".
"Again, if you have an appointment you should still attend unless contacted and told not to".
Technical staff scrambled on Sunday to patch computers and restore infected ones.
"Particularly careful clicking on links or opening attachments like a photo or a file".
Australia, according to the Prime Minister's special adviser on cyber security, Alastair MacGibbon, has missed the worst of the "WannaCry" virus - a massive global cyber "ransom" attack affecting 150 countries and hundreds of thousands of users - but he is expecting more Australian victims to turn up on Monday.
Mr MacGibbon declined to comment on the identity or type of the business impacted by the unprecedented cyber attack but said it was a small company, which did not provide critical infrastructure.
Shanghai's Fudan University received reports that a large number of school computers were infected with the virus.
He said it was too early to say who is behind the onslaught and what their motivation was.
The UK security researcher known as "MalwareTech", who helped to limit the ransomware attack, predicted "another one coming. quite likely on Monday".
"Given the potential impact to customers and their businesses, we made the decision to make the security update for platforms in custom support only, Windows XP, Windows 8, and Windows Server 2003, broadly available".
CEO Ciaran Martin said: "It is important that organisations reduce the risks of these attacks happening to them".
Instead he simply insisted the subs were "safe", adding that they operated "in isolation" when out on patrol, which possibly suggests the vessels at sea were unaffected only because they were not connected to the internet.