The letter from the Informal Anarchist Federation, or FAI, was sent to Il Secolo XIX, a local newspaper in Genoa, a port in northern Italy where two suspected FAI members shot and wounded the head of a nuclear energy company last year.
The alleged perpetrators are under arrest and the letter received by Il Secolo XIX said the parcel bomb sent to La Stampa daily on Tuesday was a form of retribution, the newspaper reported.
Il Secolo XIX also said the FAI letter included "clear threats to journalists who covered the shooting and who carry out investigations into anarchist-insurrectional movements."
It said the letter was being analyzed by police.
The FAI has been linked in recent years to a series of parcel bomb attacks against EU leaders, foreign embassies in Rome, Italian police and prison authorities. It is believed to have strong ties with Greek anarchists.
The bomb sent to La Stampa forced an evacuation of the building as bomb disposal teams were deployed.
It failed to detonate when it was opened.
Dunja Mijatovic, media freedom representative for the Organisation for Security and Co-operation in the Europe (OSCE), condemned the attempted bombing.
"All threats to media outlets represent direct threats to media freedom," he said in a statement.
"Regrettably, the event at La Stampa is only the latest in a string of cases where journalists have been attacked and intimidated in Italy," he said.
"It is a worrying trend that needs to be promptly addressed by the Italian authorities," he added.