An worldwide manhunt was under way for the plotters behind the world's biggest-ever computer ransom assault, which has hit more than 200,000 victims and has affected more than 150 countries.
Mr Smith said the "ransomware" attacks had used data stolen from the NSA earlier this year - which contained information on software vulnerabilities the government had hoped to hoard - and subsequently leaked them online.
Many firms have had experts working over the weekend to prevent new infections.
"Additionally, we have provided assistance to GP practices and worked with hospital teams across Fife to help safeguard systems".
York Teaching Hospital NHS Foundation Trust said some out-patient appointments had been cancelled on Monday, especially at Selby War Memorial Hospital, but most were not affected.
He said Europol and other agencies did not yet know who was behind the attack but "normally it is criminally minded and that is our first working theory for obvious reasons". The extortion scheme has created chaos in 150 countries and could wreak even greater havoc as more malicious variations appear.
European and British policing and security agencies have warned that the fallout from an unprecedented global cyber attack could worsen as people return to work.
Microsoft had already released a fix for the Eternal Blue vulnerability in March, but the extent of the WannaCrypt attack has highlighted how many organisations have failed to apply the fix, or are running copies of Windows that are so old that there wasn't a fix for them.
Scores of organisations inside the NHS, which provides free medical care for all and is a source of pride for Britons, were hit by the ransomware on Friday.
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 US giant.
Tom Bossert, a homeland security adviser to President Donald Trump, said "criminals" were responsible, not the US government.
For a health service, such considerations are critical.
Britain's biggest health trust, Barts Health NHS Trust, which runs five hospitals in London, said Monday it was continuing to experience some delays and disruption to services.
Victims have paid about US$30,000 in ransom so far, with the total expected to rise substantially next week, Tom Robinson, chief operating officer and co-founder of Elliptic Enterprises, a ransomware consultant that works with banks and companies, told Bloomberg.
It said in a statement: "NHS Digital issued a targeted update on a secure portal accessible to NHS staff on April 25, and then via a bulletin to more than 10,000 security and IT professionals on April 27 to alert them to this specific issue".
Brad Smith, the technology firm's president and chief legal officer, criticised United States intelligence agencies the CIA and the National Security Agency (NSA) for "stockpiling" software code which could be exploited by hackers.
The attack led to around 40 trusts across the country being shut down by what's known as ransomware - a virus that locks the user out of their computer unless they pay a fee to regain access.
The virus also has a wormlike features that looks for other vulnerable systems once it's embedded in your computer, which means it can spread to other computers in a network.