The Salafi movement and Hamas have had several collisions in the last four years.
If the claim is true, Fatah al-Islam joins a long list of radical Islamist groups that have popped up in the Gaza Strip in recent years. They include Hizb al-Tahrir (Party of Liberation), Fatah al-Yasser, Qaida al-Islam, Army of Islam, Suyuf al-Haq (Swords of Justice) and the Nasser Eddin Brigades.
This report outlines the different groups and their history in Gaza.
The jihadist firebrands, who probably number only a few hundred, are divided between three main groups ideologically aligned with al-Qaida -- Jaish al-Islam, or Army of Islam; Tawhid wa'al-Jihad, or Monotheism and Holy War; and Jaish al-Umma, or Army of the Nation.
"Their ranks may be modest in number but their capacity to shape events inside Gaza and beyond is clearly on the rise," the Financial Times observed following the slaying of Arrigoni.
Jihadist groups emerged in Gaza after Israel's unilateral withdrawal in September 2005. They expanded during the subsequent fighting between Hamas and Israel.
Hamas' cease-fire with Israel following the invasion of Gaza by 12,000 Israeli troops in late December 2008 in a 22-day invasion that killed some 1,400 Palestinians, mainly civilians, has incensed the jihadists, as has Hamas' efforts to break out of its international isolation.
What gives the growing jihadist presence even greater menace is that many recruits are former members of Hamas who say Hamas has betrayed its origins and abandoned the war against Israel.
The jihadists are believed to be responsible for many of the recent rocket and mortar attacks on Israel that have raised tensions to 2008 levels.
Ratcheting up tensions with Israel and possibly dragging Egypt into a conflict it is in no position to act on. Plus, there is the possible reciprocation of jihadist activity in Egypt.