Earlier, Health Secretary Jeremy Hunt confirmed there had not been a second wave of attacks on NHS trusts and said it was "encouraging" that the level of criminal activity was at "the lower end of the range" anticipated.
"At this stage we haven't seen the impact that they have seen in the United Kingdom, for example", Prime Minister Malcolm Turnbull told reporters in Sydney on Monday.
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 U.S. giant.
The world's biggest cyber attack launched on Friday has hit 200,000 victims in at least 150 countries.
The attack was one of the largest ransomware attacks in history.
President Donald Trump has ordered his homeland security adviser, Thomas P. Bossert, to determine what the government's response to these attacks will be, noted the Times.
Services are returning to normal, but some places are still having problems.
"We make sure the trusts are aware of their vulnerabilities and ask them to make sure they keep themselves up to date".
But NHS Grampian has opted not to name the two affected practices, which reopened yesterday morning as usual.More news: Oil rises on US inventory draw as OPEC beckons
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Liz Capp-Gray, acting director of health informatics at Medway Foundation Trust, said: "I can confirm that we have not, so far, been directly targeted by the WannaCry ransomware attack".
"The National Cyber Security Centre and the NCA (National Crime Agency) are working with Europol and other global partners", said Rudd.
May's official spokesman noted that the annual IT budget in the NHS was £4.2 billion, and an extra £50 million had been allocated to update cyber security.
Becky Pinkard, from Digital Shadows, a UK-based cyber-security firm, told AFP news agency that it would be easy for the initial attackers or "copy-cat authors" to change the virus code so it is hard to guard against.
The organisation also recommended that trusts ensure security software patches were up-to-date and that up-to-date virus software was also being used.
Microsoft took the unusual step of reissuing security patches first made available in March for Windows XP and other older versions of its operating system. We are obviously working with that business the Australian Cyber Security Centre is engaging with them'.
Additionally, experts warn that copycats could also try another attack.