It's not yet clear if companies in the Asia-Pacific region have been seriously affected.
The virus's pace appeared to slow by June 28, partly because the malware appeared to require direct contact between computer networks, a factor that may have limited its spread in regions with fewer connections to Ukraine.
The malware's origins remain unclear.
Ben Johnson spoke with Chester Wisniewski, a senior security researcher at Sophos, a network security company.
Mondelez, the company that owns Oreos, Cadbury and many other global snack brands, reported a computer outage across its global operations.
Ukraine's central bank said several lenders had been hit in the country, hindering operations and leading the regulator to warn other financial institutions to tighten security measures.
The "Petya" ransomware has caused serious disruption at large firms including the advertising giant WPP, French construction materials company Saint-Gobain and Russian steel and oil firms Evraz and Rosneft. Kaspersky said the "NotPetya" attack had hit 2,000 users in Russia, Ukraine, Poland, France, Italy, the UK, Germany and the US. There are now reports of attacks in the US. A spokeswoman for Heritage Valley Health System would say only that operational changes had to be made. The global cyberattack is similar to a recent WannacCry ransomware that crippled over 300,000 computers worldwide.
It also spread using MeDoc. There have also been reports that multiple USA companies have been disrupted by the attack.
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Because the ransomware used at least two other ways to spread on Tuesday - including stealing victims' credentials - even those who used the Microsoft patch could be vulnerable and potential targets for later attacks, researchers at F-Secure, a Finnish cybersecurity firm, and others told The New York Times.
"Once activated, the virus can automatically and freely distribute itself on your network", Ukraine's cyberpolice tweeted. Self-spreading software, often described as "worms", are particularly feared because they can spread rapidly, like a contagious disease. "It's like somebody sneezing into a train full of people", he said.
But Microsoft says the ransomware is "a new variant" of Petya, adding that it has issued new security updates to protect computers running its Windows software.
Unlike WannaCry, the software is created to spread across PCs in a contained network, not the whole internet.
"We are talking about a cyberattack", said Anders Rosendahl, a spokesman for the Copenhagen-based shipping group. In a telephone interview, Bitdefender analyst Bogdan Botezatu said that he had examined samples of the program and that it appeared to be almost identical to GoldenEye, one of a family of hostage-taking programs that has been circulating for months.
The cryptolocker demands $300 in bitcoins and does not name the encrypting program, which makes finding a solution hard, Group IB spokesman Evgeny Gukov said.
Ukrainian Prime Minister Volodymyr Groysman called the ransomware campaign "unprecedented", but said "vital systems haven't been affected".