"It does not look like the numbers are rising as we expected," Europol spokesperson Claire Georges told ABC News, referring to the number of victims struck by what Europol has called an "unprecedented" attack.
Users appear to have upped their security in the wake of the May 12 attack, Georges said. Experts had feared the "WannaCry" virus would unleash another round of chaos on Monday as a new workweek begins.
"It might be sitting on many computers in sectors, in companies over the weekend and when they're switched on again Monday morning we might see the infection rates going back up," Europol Director Rob Wainwright said.
But fears of another immediate wave of infections in Europe didn't appear to have become reality.
Thousands of users on Friday received the message "Oops, your important files are encrypted" along with threats from the hackers who encrypt computer files so they can't be accessed and threaten to delete them unless a ransom of up to $300 or more in Bitcoins is paid.
The perpetrators remain a mystery.
"All of the police forces in Europe are working together to find out the identity of the hackers," Georges, the Europol spokesperson, said. "We've seen a very big response from key public and private parties. It has been a good success in terms of international cooperation."
"We are very busy at the moment," Georges said.
ABC News' Brian Ross, Rhonda Schwartz, James Gordon Meek, Dean Schabner and Maia Davis contributed to this report.