Police reported three separate episodes at different locations early on Saturday which caused delays of up to 2-1/2 hours for high-speed and regional services, particularly around the city of Bologna.
No one was injured and no trains were damaged.
In a statement circulated online, an anarchist group said a progressive crackdown on demonstrations by Prime Minister Giorgia Meloni had made confrontation on the streets "ineffective" and meant they had to find other forms of protest.
"It therefore seems necessary to adopt clandestine methods, decentralise the conflict and multiply its fronts, and turn to self-defence and sabotage in order to survive the times ahead," the anarchist statement said.
There was no immediate comment from the police on the statement. Deputy Prime Minister Matteo Salvini, who heads the Transport Ministry, vowed to catch the anarchists.
"We will do everything to ... hunt down and flush out these thugs wherever they hide, to put them in prison and to confront those who defend them," he wrote on X.
"Long live the Olympics, symbol of an Italy that builds, that inspires emotion, that never gives up," he added.
The anarchists denounced the Olympic Games as a "glorification of nationalism", saying the event provided a "testing ground" for policing crowds and monitoring movement.
Shortly after Saturday's attack on rail infrastructure, a small group of around 100 hooded protesters threw flares and fireworks at police after breaking away from the main body of an anti-Olympics demonstration in Milan, a co-host of the Games.
Meloni condemned on Sunday the street protesters and the saboteurs as "enemies of Italy".
(Reporting by Crispian Balmer; Editing by Alison Williams)
Riot police officers keep watch on a marching group following an attack on a police car in front of the police headquarters in Turin, northern Italy, 28 February 2024. A group of autonomists and anarchists carried out an attack on a State Police patrol that was taking a man of Moroccan origins to a repatriation center in Lombardy to be expelled from Italy. Interior Minister Matteo Piantedosi said that he is 'outraged by the very serious attack on a police vehicle' in the center of Turin. A policeman was slightly injured in the riots. EPA/ALESSANDRO DI MARCO