The attacks came in the form of ransomware, a technique used by hackers that locks users' files unless they pay the attackers a designated sum in the virtual currency Bitcoin.
The scope of the attacks was not immediately clear, but some analysts reported that dozens of countries had been affected, with the malware linked to attacks on hospitals in Britain as well as the Spanish telecom giant Telefonica and the US delivery firm FedEx.
The US Department of Homeland Security's computer emergency response team said it was aware of ransomware infections "in several countries around the world."
"We are now seeing more than 75,000 detections... in 99 countries," Jakub Kroustek of the security firm Avast said in a blog post around 2000 GMT.
Earlier, Kaspersky researcher Costin Raiu cited 45,000 attacks in 74 countries, saying that the malware, a self-replicating "worm," was spreading quickly.
Russia's interior ministry says computers hit by 'virus attack'
Russia's interior ministry said Friday that some of its computers had been hit by a "virus attack" amid reports of major cyber strikes across the globe.
Ministry spokeswoman Irina Volk told Russian news agencies it had "recorded a virus attack on the ministry's personal computers controlled by a Windows operating system."
"The virus has been localised. Technical work is under way to destroy it and renew the means of virus protection," she said.
Volk added that some 1,000 computers -- less than one percent of their total number -- had been affected, Interfax reported.
An unnamed source told Interfax that the attack had not led to any information leaks.
The ministry's statement comes as an increasing number of cyber strikes are reported around the world, including against dozens of British hospitals.
Russian telecom operator MegaFon said it had also been victim of a cyber attack on Friday that interrupted the work of its call centres.
"We needed to partly turn off whole networks internally so the virus didn't spread," RIA Novosti news agency quoted MegaFon public relations director Pyotr Lidov as saying.
Forcepoint Security Labs said that "a major malicious email campaign" consisting of nearly five million emails per hour was spreading the new ransomware.
The malware's name is WCry, but analysts were also using variants such as WannaCry.
Forcepoint said in a statement that the attack had "global scope", affecting organisations in Australia, Belgium, France, Germany, Italy and Mexico.
In the United States, FedEx acknowledged it had been hit by malware and was "implementing remediation steps as quickly as possible."
The UK's state-run National Health Service declared a "major incident" after the attack, which forced some hospitals to divert ambulances and scrap operations.
In Spain, major firms including Telefonica were hit, with employees told to shut down workstations immediately through megaphone announcements.
'Direct infection'
At least 16 organisations within the NHS, some of them responsible for several hospitals each, reported being targeted.
"We are aware that a number of NHS organisations have reported that they have suffered from a ransomware attack. This is not targeted at the NHS, it's an international attack and a number of countries and organisations have been affected," said Prime Minister Theresa May.
Britain's National Cyber Security Centre and its National Crime Agency were looking into the UK incidents.
Pictures posted on social media showed screens of NHS computers with images demanding payment of $300 (275 euros) in Bitcoin, saying: "Ooops, your files have been encrypted!"
It demands payment in three days or the price is doubled, and if none is received in seven days, the files will be deleted, according to the screen message.
A hacking group called Shadow Brokers released the malware in April claiming to have discovered the flaw from the NSA, Kaspersky said.
Although Microsoft released a security patch for the flaw earlier this year, many systems have yet to be updated, researchers said.
"Unlike most other attacks, this malware is spreading primarily by direct infection from machine to machine on local networks, rather than purely by email," Lance Cottrell, chief scientist at the US technology group Ntrepid.
"The ransomware can spread without anyone opening an email or clicking on a link."
Ambulances diverted
NHS Incident Director Anne Rainsberry urged the British public to "use the NHS wisely while we deal with this major incident which is still ongoing".
The sort of ransom demands seen on the NHS screens are not without precedent at medical facilities. In February 2016, a Los Angeles hospital, the Hollywood Presbyterian Medical Center, paid $17,000 in Bitcoin to hackers who took control of its computers for more than a week.
"Ransomware becomes particularly nasty when it infects institutions like hospitals, where it can put people's lives in danger," said Kroustek, the Avast analyst.
A spokesman for Barts Health NHS Trust in London said it was experiencing "major IT disruption" and delays at all four of its hospitals.
"We have activated our major incident plan to make sure we can maintain the safety and welfare of patients," the spokesman said. "Ambulances are being diverted to neighbouring hospitals."
Two employees at St Bartholomew's Hospital, which is part of Barts Health, told AFP that all the computers in the hospital had been turned off.
Caroline Brennan, 41, went to the hospital to see her brother, who had open heart surgery.
"They told us there was a problem. They said the system was down and that they cannot transfer anyone till the computer system was back up so he is still in the theatre."
