The murder drew widespread condemnation, from Gaza City to Italy.
Hamas called it a "heinous crime" and vowed to hunt down the perpetrators, while Italy decried an "act of vile and senseless violence."
Arrigoni's friends and family were devastated, and spoke of their shock that the killers had targeted "a real activist for Palestinian human rights."
In a video posted on YouTube, the kidnappers said Arrigoni had been taken hostage in order to secure the release of an unspecified number of Salafists detained by Hamas, including Hisham al-Saedini, a leader of the radical group Tawhid wal Jihad.
The kidnappers, who said they belonged to 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.
Tawhid wal Jihad denied it had anything to do with the kidnapping, while acknowledging that the murder was the result of Hamas's "repression" of Salafists.
"What happened is the natural result of the repressive policy of Hamas and its government against the Salafists," it said.
"We and others have for a long time warned the Hamas government against the risks of acting... against the Salafist trend."
In Gaza City, Hamas officials said two people had been arrested on suspicion of involvement in the kidnapping and said they were hunting further accomplices to what spokesman Ihab al-Ghussein called a "heinous crime which has nothing to do with our values, our religion, our customs and traditions.
"The other members of the group will be hunted down," he said.
Italy's foreign ministry expressed "deep horror over the barbaric murder," saying it was an "act of vile and senseless violence committed by extremists who are indifferent to the value of human life."
Arrigoni's kidnappers described him as a "journalist who came to our country for nothing but to corrupt people" -- a charge completely rejected by activists and aid workers who knew him in Gaza.
"He's very well-known, he lives among the people," said Huwaida Arraf, a co-founder of ISM. "Vit has repeatedly put his life in danger, put his life on the line in support of the Palestinians."
A journalist colleague at the Italian daily Il Manifesto said he was "astounded" by Arrigoni's death.
"We're also wondering how a pacifist who was wholeheartedly pro-Palestinian could be killed by Palestinians, even though you have to ask who those Palestinians were," Maurizio Matteuzzi, foreign affairs journalist with the left-leaning paper, told AFP.
In Jerusalem, shocked Italian volunteers who had just left Gaza converged on a hotel in the city's annexed eastern sector, the horror evident upon their faces.
"He was a lively, lovely person, we made fun of him because he was more Palestinian than Italian," said Simona Ghizzoni, a 34-year-old photographer who worked in Gaza for the Italian NGO Cospe.
"He was a real believer and a real activist for Palestinian human rights."
Leaving Gaza, she said, was the result of "a strong suggestion" from the Italian embassy.
"When we got to the Palestinian checkpoint before Erez, there were all these Palestinians coming and saying 'We are sorry, we are sorry.' All the Palestinians I met are completely shocked and sad," she said.
Arrigoni is the third ISM member to be killed in Gaza -- US national Rachel Corrie was crushed to death by an Israeli bulldozer in March 2003, and a month later Briton Tom Hurndall was shot and critically injured by the army. He died in January 2004.
In Gaza City, several hundred people rallied in the Square of the Unknown Soldier against the killing, while in the West Bank, around 100 people, most of them foreigners, marched through Ramallah to a house of mourning in El Bireh, an AFP correspondent said.