Bossert said "criminals" are responsible, not the US government.
It says the latest virus exploited flaws in Microsoft Windows identified by and stolen from USA intelligence services. Indonesia's government reported two hospitals in Jakarta were affected.
Global cyber chaos was spreading Monday as companies booted up computers at work following the weekend's worldwide "ransomware" cyberattack.
The cyber attack that crippled NHS computer systems is the biggest of its kind ever launched, security chiefs have said.
Microsoft's president and top lawyer said Sunday that the ongoing cyberattacks, which experts are calling the largest in history, should be a "wake-up call" for governments - especially the U.S.
'The governments of the world should treat this attack as a wake-up call.
The cyber attack which hit the NHS was a ransomware attack which encrypts files on a user's computer, blocking them from view and threatening to delete them unless a payment is made.
They advised those whose networks have been effectively shut down by the ransomware attack not to make the payment demanded - the equivalent of $300, paid in the digital currency bitcoin.
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The NHS was among hundreds of organisations affected around the world, with 47 trusts hit.
Experts urged organizations and companies to immediately update older Microsoft operating systems, such as Windows XP, with a patch released by Microsoft Corp.to limit vulnerability to a more powerful version of the malware - or to future versions that can't be stopped.
This is according to Andrew Potgieter, Security Solutions Director at Westcon-Comstor Southern Africa, who adds that even more unnerving is that "kits" to put together attacks of this nature are readily available for download on the Internet and doesn't require a group of elite hactivists to run.
While the scale of the attack shows Microsoft needs to strengthen its own capabilities, "there is simply no way for customers to protect themselves against threats unless they update their system", Smith said in his blog post.
Speaking on ITV's Peston on Sunday, Mr Wainwright said: "At Europol, we are running around 200 global operations against cyber crime each year".
Spanish firm Telefonica, French automaker Renault, the US -based delivery service FedEx and the German railways Deutsche Bahn were among those affected.
Researchers who helped prevent the spread of the malware and cybersecurity firms worked around the clock over the weekend to monitor the situation and install the software patch.
Prasad said the government was working hard to promote Digital India throughout the country. More action is needed, and it's needed now.
"Our Data Security Centre continues to work around the clock alongside the National Cyber Security Centre, to support NHS organisations that have reported any issues related to this cyber-attack", the body said - alongside issuing guidance on protecting against the cyberattack, explaining which patches to apply.