"It was clear warnings were given to hospital trusts but this is not something that focused on attacking the NHS here on the United Kingdom". There is concern that family doctors' surgeries could be struck on Monday when they open.
The British government said 48 of 248 health service trusts - the bodies that run the hospitals - in England had been impacted by Friday's attack.
On Monday, the opposition Labour Party said Prime Minister Theresa May's response to the crisis had been poor and her government was to blame for failing to invest to keep the service secure.
Cyber security experts worked through the weekend alongside the National Cyber Security Centre (NCSC), part of the GCHQ spy agency, to patch computer systems but some hospitals still cautioned patients on Monday to only seek treatment for life-threatening emergencies.
"We haven't seen a second spike in #WannaCry #ransomware attacks, but that doesn't mean there won't be one", the NCA, said on Twitter.
In a snap election campaign which May has dominated so far, the debate over the cyber attack on the NHS forced her onto the defensive, although it was not immediately clear what impact, if any, it would have on her popularity.
"Staff are working hard to ensure that the small number of organisations still affected return to normal shortly".
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".
"There are things you can do that everyone can do (.) in particular making sure that our data is properly backed up and making sure that we are using the software patches", he said.
NHS cyber attack - fallout continues
Carmaker Renault said one of its French plants, which employs 3,500 people, was not reopening Monday as a "preventative step". But, he added, state and local governments that lack expertise or funding may face greater troubles.
NHS Digital said it had made health trusts aware last month of IT protection that could have prevented the damage.
He added the attack "was not specifically targeted at the NHS and is affecting organisations from across a range of sectors".
"These alerts included a patch to protect their systems".
Seven hospital trusts were still experiencing problems earlier on Monday, among them St Bartholomew's Hospital in London, and Southport and Ormskirk Hospital NHS Trust.
Problems with cyber security in the NHS was highlighted previous year by Dame Fiona Caldicott, the national data guardian, who warned issues were given insufficient priority and that health bodies persisted in using obsolete computer systems, The Times reported.
Labour has accused the Government of a "chaotic" response to the cyberattack, and claimed cuts had left hospitals "wide open" to being compromised.
Asked if warnings had been ignored, Mrs May said: "No".
"The reason why so many patients have been unaffected today is because they were ready for this", she said.
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