A third terrorist committed suicide rather than being taken prisoner, Hamas said.
A conflicting report said two terrorists were slain during the Hamas raid on the Tawhid wal-Jihad cell.
Arrigoni, 36, had lived in Gaza since arriving in 2008 aboard a a boat purported to be carrying humanitarian aid. Israel had allowed the boat to pass despite the naval blockade on the territory.
Hamas Interior Ministry spokesman Ihab Ghussein said police stormed the house Tuesday evening after a fierce firefight. One of the terrorists, Ghussein claimed, threw grenades at his two associates, wounding them, and then shot and killed himself.
Five other Hamas policemen and a girl caught in the crossfire were injured as well.
According to Ghussein, Hamas security forces surrounded a building in Nuseirat in central Gaza in order to capture the Tawhid wal-Jihad cell. Tawhid wal-Jihad is a Salafist jihadi group associated with Al-Qaeda which has been attracting followers and is seen by Hamas as a competitor for populist support in Gaza.
Before the firefight a statement from the Hamas-run Interior Ministry declared the area a closed security zone "because of the suspicion of the presence of the fugitives." Roads leading to the four-story building were blocked by security forces.
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Meanwhile, Hamas reported Tuesday that a Gaza Arab, Adel Rizk, died shortly after interrogation by Hamas security personnel. According to Hamas the 52-year-old died on Tuesday in a hospital after falling ill during his interrogation. Hamas did not specify the cause of death or say why Rizk was detained.
Rizk's brother, Moean, said Adel was healthy when Hamas arrested him last week. Moean also said he and his brother had been arrested several times since Hamas violently seized control of Gaza in 2007 for suspicion of passing information to Hamas' archrival, the Fatah-run Palestinian Authority.