However staff beginning the working week have been told to be careful.
The WannaCry ransomware started taking over users' files on Friday, demanding $300 (£230) to restore access.
Hundreds of thousands of computers have been affected so far. Computer giant Microsoft said the attack should serve as a wake-up call.
BBC analysis of three accounts linked to the ransom demands suggests only about $38,000 (£29,400) had been paid by Monday morning.
However, the ransomware warning said that the cost would double after three days, so the payments may increase.