The worldwide crime-fighting organisation has also revealed there were 200,000 victims in 150-plus countries in Friday's attack.
He warned the threat could escalate further and expressed concerns over possible attacks on Monday.
He warned that more people may be hit by the virus Monday when they return to work and switch on their computers. "They're processing a lot of sensitive data", he said.
Speaking to British ITV channel, Rob Weinwright said the attack had so far affected more than 100,000 organizations in 150 countries.
On Sunday, Chinese media reported that the virus attacked many university networks in China.
Meanwhile, Turkey's Information and Communications Authority BTK said on Saturday an operation to prevent further spread of the malware continued and urged people to update their antivirus programs and scan their computer systems.
A Jakarta hospital said on Sunday that the cyber virus had infected 400 computers, disrupting the registration of patients and finding records.
As terrifying as the unprecedented global "ransomware" attack was, cybersecurity experts say it's nothing compared to what might be coming - especially if companies and governments don't make major fixes.
NHS staff shared screenshots of the WannaCry programme, which demanded a payment of $300 (£230) in virtual currency Bitcoin to unlock the files for each computer.
Russia's cybersecurity monitoring center, FinCert, operated by the country's central bank, also announced that the attack had not penetrated its systems.
Cyber security experts say the spread of the virus dubbed WannaCry - "ransomware" which locked up computers in vehicle factories, hospitals, shops and schools in several countries - has slowed, but that any respite might be brief.
Soon he and MalwareTech were communicating about what they'd found: That registering the domain name and redirecting the attacks to MalwareTech's server had activated the kill switch, halting the ransomware's infections.
Oliver Gower, of the UK's National Crime Agency, said: "Cyber criminals may believe they are anonymous but we will use all the tools at our disposal to bring them to justice". All sectors of the economy were vulnerable and organizations could take lessons from the banking industry, which appeared to have largely escaped the global attack.
He said few banks in Europe had been affected, having learned through the "painful experience of being the number one target of cybercrime" the value of having the latest cyber security in place.
But he also said he's concerned the authors of the malware could re-release it - perhaps in the next few days or weeks - without a kill switch or with a better one, or that copycats could mimic the attack.
Wainwright said Europol did not know the motive. Several cybersecurity firms said they had identified the malicious software behind the attack, which has apparently hit Russian Federation the hardest.
"The problem is the larger organizations are still running on old, no longer supported operating systems", said Lawrence Abrams, a New York-based blogger who runs BleepingComputer.com.
Russia's health ministry said its attacks were "effectively repelled".
Security experts said the attack appeared to be caused by a self-replicating piece of software that enters companies and organisations when employees click on email attachments, then spreads quickly internally from computer to computer when employees share documents and other files.
Dr Jakobsson said: "There's absolutely no excuse for any business not to have up to date systems".
A top Russian mobile operator said Friday it had come under cyberattacks that appeared similar to those that have crippled some United Kingdom hospitals.
"This attack is going to be a wake-up call for many businesses that have dragged their feet when it comes to security and updating their systems", Bazley said.