In Britain, whose health service was among the first high-profile targets of the online extortion scheme, Health Secretary Jeremy Hunt said "we have not seen a second wave of attacks".
"The vast majority of patients have noticed no difference".
A total of 48 trusts in England, as well as 13 NHS bodies in Scotland have been hit by Friday's attacks, resulting in cancelled operations and appointments, a loss of access to important medical records, and in some cases, the diversion of emergency services.
"We should expect similar attacks regularly in the coming days and weeks", said Giullaume Poupard, head of French government cyber security agency ANSSI.
It said patients with appointments today should go to the hospital on Coreys Mill Lane as normal unless told otherwise.
Tayo Dada, a Christian and ex-hacker who now runs Managed IT Services, told Premier: "There is definitely a massive, exponential rise in the number of hacking attacks. but, unfortunately, people are not taking the proactive steps in order to ensure they are being a lot more suspicious about what files they're opening and how they secure their networks".
While hospitals have been working throughout the weekend to get their IT systems up and running, some trusts are still dealing with the cyber attack. "Which we will", she said.
At Indonesia's biggest cancer hospital, Dharmais Hospital in Jakarta, around 100-200 people packed waiting rooms after the institution was hit by cyber attacks affecting scores of computers.
A Japanese non-profit says computers at 600 locations had been hit in the global "ransomware" cyberattack.
He added: "We will provide a public update should the situation change".
In a statement this morning, the trust said that it was no longer diverting ambulances away from any of its hospitals and that trauma and stroke care is also fully operational.
The cyberattacks started Friday and spread rapidly around the globe using a security flaw in Microsoft's Windows XP operating system, an older version that is no longer given mainstream tech support by the U.S. giant.
But NHS Digital said it had made health trusts aware last month of IT protection that could have prevented the attack.
The enterprise-security division of Qihoo 360, one of the country's leading suppliers of anti-virus software, said 29,372 institutions ranging from government offices to universities, ATMs and hospitals had been "infected" by the outbreak as of late Saturday.
This operating system is no longer supported by Microsoft, and so does not routinely receive security updates created to protect against such attacks.
President Donald Trump ordered his homeland security adviser, Tom Bossert, to hold an emergency meeting Friday night to assess the threat posed by the cyberattack, senior administration official told Reuters.
Blackpool Teaching Hospitals NHS Foundation Trust, NHS Blackpool Clinical Commissioning Group (CCG) and NHS Fylde and Wyre CCG are still experiencing IT problems.
"We take cyber security seriously", she said, while highlighting the global nature of the attack.
However Ms Rudd strongly denied warnings had been ignored.
"The government's response has been chaotic, to be frank", the British Labour Party's health spokesman Jon Ashworth said.
Putin said Russian Federation had a year ago sought an agreement with the previous United States administration on co-operation in the field of cyber security, but Washington had dragged its feet and no deal was concluded.