The ransomware attack carried out Friday has hit some 200,000 hospitals, companies and government offices in more than 150 countries.
Lynne Owens, director-general of Britain's National Crime Agency, said there was no indication of a second surge in the cyberattack but warned, "That doesn't mean there won't be one".
Europol said a special task force at its European Cybercrime Centre was "specially created to assist in such investigations and will play an important role in supporting the investigation".
"Of course there are amounts that are being demanded, in this case relatively small amounts - US$300 rising to US$600 if you don't pay within three days", he said. Some security experts calculate that ransomware may bring in as much as $1bn/year in revenue for the attackers.
The WannaCry attack should give urgency to boosting cyber security.
In China, state media said more than 29,000 institutions there had been infected along with hundreds of thousands of devices.
"The U.S.is still in a relatively good place - I don't want to jinx it", the department official says.
Ryan Kalember, senior vice-president at Proofpoint Inc., which helped stop its spread, said the version without a kill switch could spread.
While the scale of the attack shows Microsoft needs to strengthen its own capabilities, "there is simply no way for customers to protect themselves against threats unless they update their system", Smith said in his blog post.
Ransomware known as "WannaCry" was unleashed on Friday and exploited vulnerabilities in outdated versions of Microsoft Windows.
"In particular, making sure that our data is properly backed up and making sure that we are using the software patches, the anti-virus patches, that are sent out regularly by manufacturers".
The U.S. government clearly had its priorities wrong in not focusing on better protecting these cyberweapons, he said. The country's banking system was also attacked, although no problems were detected, as was the railway system.
Nissan: The carmaker said in a statement that "some Nissan entities were recently targeted" but "there has been no major impact on our business". Universities in Greece and Italy also were hit.
In 2016, Motherboard reported hospitals across the United Kingdom run old, outdated Windows systems - legacy technology that no longer receives updates.
"For now, it does not look like the number of infected computers is increasing", said a Europol spokesman.
Kaspersky said it was "trying to determine whether it is possible to decrypt data locked in the attack - with the aim of developing a decryption tool as soon as possible".
Fortunately, a 22-year-old British researcher and 20-something American security engineer discovered a "kill switch" and unregistered domain that halted the attack, reports the Associated Press. "Since this WannaCry attack has been so effective thus far, it is quite likely that this is the first of many ransomware attacks that leverage exploits to effectively spread their payloads throughout the Internet".
"You are dealing with a criminal", he said.