It is the largest ransomware attack observed in history.
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".
Images appeared on victims' screens demanding payment of $300 (275 euros) in Bitcoin, saying: "Ooops, your files have been encrypted!"
Reports indicate that payments of over $38,000 dollars have been made to the hackers as the ransomware threatened to double prices after three days and to delete files after seven days.
The Japan Computer Emergency Response Team Coordination Center said 2,000 computers in Japan were reported affected so far, citing an affiliate foreign security organization that it can not identify.
Experts and officials offered differing estimates of the scope of the attacks, but all agreed it was huge.
The UK government has insisted that the NHS had been repeatedly warned about the cyber threat to its IT systems, with Defence Secretary Michael Fallon stating 50 million pounds was being spent on NHS systems to improve their security.
Investigators are working to track down those responsible for the ransomware used on Friday, known as Wanna Decryptor or WannaCry.
Dr Krishna Chinthapalli, a neurology registrar at the National Hospital for Neurology and Neurosurgery in London, had warned that an increasing number of hospitals could be shut down by ransomeware attacks in an article on the vulnerability of the NHS network in the "British Medical Journal" on Wednesday, two days before the major cyber-hack.
"We've seen what happens when the US NSA (National Security Agency). develops hacking tools, effectively weapons for breaking in to ordinary people's computers then loses control of one of those exploits that has then been effectively weaponised by a criminal organisation that is now seeking to ransom people", he told reporters. Governments can act to enforce cybersecurity protective measures on companies, especially those that provide critical services or infrastructure.
Microsoft said in a blog post that it was taking the "highly unusual" step of providing the patch for older versions of Windows it was otherwise no longer supporting, including Windows XP and Windows Server 2003.
"In addition to protective real-time monitoring of national NHS IT services and systems, which were unaffected by this issue, we are supporting NHS organisations by undertaking cyber security testing and providing bespoke advice and action points".
The companies and government agencies targeted were diverse.
"Once we get to the bottom of this one, we'll make sure that this is available to people as well", he said.
Russia's interior ministry said some of its computers had been hit by a "virus attack" and that efforts were underway to destroy it.
Russian Federation said its banking system was among the victims of the attacks, along with the railway system, although it added that no problems were detected.
Deutsche Bahn: The German railway company told CNNMoney that due to the attack "passenger information displays in some stations were inoperative" as were "some ticket machines". Universities in Greece and Italy also were hit.
Microsoft fixed MS17-010 in its March release, but it is likely that the NHS and other affected entities did not patch their devices in time to counter the attack. "You're only safe if you patch as soon as possible", he tweeted.
A 22-year old security researcher in the United Kingdom discovered a "kill-switch" to initially stop the spread of the attack.