The attacks affected 150 countries and infected at least 200,000 computers worldwide, despite global cyber security firms warning last month that they were expected.
Queen Alexandra Hospital in Portsmouth was unaffected by the attack.
"We will get a decryption tool eventually, but for the moment, it's still a live threat and we're still in disaster recovery mode", Europol director Rob Wainwright told CNN's Becky Anderson on Sunday, adding that the number of cases was still rising.
The Home Secretary Amber Rudd will hold a meeting of the emergency COBRA committee later today.More news: National Basketball Association playoffs 2017: Cavaliers never trail in Game 1 blowout over Celtics
The WannaCry or WannaCrypt ransomware attack deployed a Windows exploit that the National Security Agency had used for its own purposes until it was leaked in April by the hacking group Shadow Brokers. "Which we will", she said.
The organisation told trusts: "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".
Mr Biggs said: "It is vital that NHS trusts invest adequately in cyber security as they seek to protect themselves against future attacks".
The internet connection was back up yesterday and the hospital said patients, who were still able to text or phone, weren't affected over the weekend.More news: New Video Shows Erdogan Watching Washington Brawl
"There are clearly going to be some small businesses impacted ... but as a whole of nation, we can be confident so far that we've missed the worst of this".
'There has been one incident of the ransomware hitting a business here in Australia and there could be two other incidents where it has occurred although we are trying to confirm that, ' he said.
It comes as the former United States national intelligence director said the global "ransomware" attack could grow much larger when people return to work.
In light of the attack, justice secretary Michael Matheson said the Scottish Government is taking action to enhance security, including contacting more than 120 public bodies to ensure they have appropriate defences in place.More news: Worldwide ransomware cyberattacks: What we know
"Although we have never seen anything on this scale when it comes to ransomware attacks, they are relatively common and there are things that you can do, that everyone can do, all of us can do, to protect ourselves against them", he said.
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