The Al-Tawhid Wal-Jihad group said that Arrigoni's abduction and slaying on Friday was "natural conclusion to the Hamas government policy against other organisations within the Strip," Maan news agency reported.
"While denying all reponsibility for the death of Arrigoni, we reaffirm our will to wage holy war," said a message from a second Salafite group, The Lions of the Mujahadeen of Palestine.
There are five Palestinian Salafite groups in Gaza, whose austere form of Islam and and refusal to abide by various cease-fires with Israel have brought them into conflict with Gaza's ruling Islamist group Hamas.
Arrigo's lifeless body was found by Hamas security agents in a house in north Gaza on Friday. Hamas said he had been hanged, while other reports claimed he had been suffocated.
Arrigoni's murder followed his abduction late on Thursday. In a YouTube clip posted earlier by his abductors, Arrigoni was shown blindfolded with a bloody right eye and a hand could be seen pulling his head up by his hair to face the camera.
In the video, the kidnappers said Arrigoni had been taken hostage in order to secure the release of an unspecified number of their members detained by Hamas security forces, including a jihadist leader called Sheikh Hisham al-Suedani.
"The Italian hostage entered our land only to spread corruption," read an accompanying Arabic text. It described Italy as "the infidel state".
The kidnappers, who identified themselves as Salafists belonging a group calling itself The Brigade of the Gallant Companion of the Prophet Mohammed bin Muslima, said they would execute Arrigoni if their demands were not met by 5:00 pm (1400 GMT) on Friday.
It was unclear why the militants killed Arragoni before the expiry of the deadline.
The murder of Arrigo, who had been in Gaza for three years, drew condemnation from the Italian government, from Hamas, and from the International Solidarity Movement for which he worked.