There are fears of more "ransomware" attacks as people begin work on Monday, although few have been reported so far.
Many firms have had experts working over the weekend to prevent new infections. The virus took control of users' files and demanded $300 (£230) payments to restore access.
The spread of the virus slowed over the weekend but the respite might only be brief, experts have said. More than 200,000 computers have been affected so far.
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Australian officials said so far only three small-to-medium sized businesses had reported being locked out of their systems while New Zealand's ministry of business said a small number of unconfirmed incidents were being investigated.
In Japan, both Nissan and Hitachi reported some units had been affected, while in China energy giant PetroChina said that at some petrol stations customers had been unable to use its payment system.
'Like stealing Tomahawks'
A statement from Microsoft president and chief legal officer Brad Smith on Sunday criticised the way governments store up information about security flaws in computer systems."We have seen vulnerabilities stored by the CIA show up on WikiLeaks, and now this vulnerability stolen from the NSA has affected customers around the world," he wrote.