"We are aware that a number of NHS organisations have reported that they have suffered from a ransomware attack. This is not targeted at the NHS, it's an international attack and a number of countries and organisations have been affected," May said, referring to the country's National Health Service.
The state-run NHS declared a "major incident" after the cyber attacks, which prompted some hospitals to divert ambulances and scrap operations.
"The National Cyber Security Centre is working closely with NHS digital to ensure that they support the organisations concerned and that they protect patient safety," May added.
At least 16 organisations within the NHS, some of which are responsible for several hospitals each, have reported being struck.
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Following the cyber attacks pictures were posted on social media showing screens of NHS computers with images demanding payment of USD 300 (275 euros) worth of the online currency Bitcoin, saying: "Ooops, your files have been encrypted!"
Forcepoint Security Labs said that "a major malicious email campaign" consisting of nearly five million emails per hour was spreading the new ransomware.
The group said in a statement that the attack had "global scope", affecting organisations in Australia, Belgium, France, Germany, Italy and Mexico.