British advertising giant WPP and the French industrial group Saint-Gobain said they came under attack and put protection protocols in place to avoid data loss.
Robin Dargue, WPP's group chief information officer, has notified agencies that a number of companies within the group have been hit with a ransomware virus.
Danish shipping company Maersk said systems were down across multiple sites, while the virus also reached servers for the Russian oil company Rosnoft.
The British National Cyber Security Centre said it was "aware of the global ransomware incident" and is "monitoring the situation closely".
"There have been indications of late that Petya is in circulation again, exploiting the SMB (Server Message Block) vulnerability," the Swiss Reporting and Analysis Centre for Information Assurance (MELANI) said in an email.
Ukraine's prime minister says that a cyberattack affecting his country is "unprecedented," but "vital systems haven't been affected."
Prime Minister Volodymyr Groysman also said on Facebook that "our IT experts are doing their job and protecting critical infrastructure ... The attack will be repelled and the perpetrators will be tracked down."
Ukrainian Deputy Prime Minister Pavlo Rozenko on Tuesday posted a picture of a darkened computer screen to Twitter, saying that the computer system at the government's headquarters has been shut down.
There's very little information about who might be behind the disruption, but technology experts who examined screenshots circulating on social media said it bears the hallmarks of ransomware, the name given to programs that hold data hostage by scrambling it until a payment is made.
The scale and use of ransomware has similarities to last month's cyber attack, which some experts linked to North Korea.
This hit dozens of countries and used a flaw that was once incorporated inside the National Security Agency's surveillance tool kit.
The world is still recovering from last month's WannaCry or WannaCrypt virus, which brought the UK'S NHS to its knees.
