The hacking attack sought to exploit a software vulnerability, ACN director general Roberto Baldoni told Reuters, adding it was on a massive scale.
Italy's ANSA news agency, citing the ACN, reported that servers had been compromised in other European countries such as France and Finland as well as the United States and Canada.
Dozens of Italian organisations were likely to have been affected and many more had been warned to take action to avoid being locked out of their systems.
US cybersecurity officials said they were looking into the reported incidents.
"CISA is working with our public and private sector partners to assess the impacts of these reported incidents and providing assistance where needed," the US Cybersecurity and Infrastructure Security Agency (CISA) said.
Thousands of Telecom Italia customers across Italy complained of internet outages and glitches on the weekend, which the company blamed on problems with an international link.
Users from the northern city of Milan to the Sicilian capital Palermo reported problems on Sunday, with the issue mainly focused on fixed-line internet services.
Numerous football fans bemoaned interruptions to their streaming of the Serie A game between Spezia and league leaders Napoli.
"An international interconnection problem impacting the service at national level was detected. Analyses are underway to resolve the problem," a TIM spokesperson said.
There was no indication that the problems were caused by hackers, ANSA reported.
TIM, Italy's former telecoms monopoly, is at the centre of a takeover struggle, with private equity group KKR having made a non-binding bid to buy its network.
AAP
