After a Katyusha rocket fired from Lebanon landed in Israel last month, Prime Minister Benjamin Netanyahu blamed Hezbollah, the Shiite militia, and its Iranian backers. But Israeli security officials attributed the attack, as well as a similar one in August, to a Sunni jihadist group linked to Al Qaeda.

That disconnect is representative of the deepening dilemma Israel faces as the region around it is riven by sectarian warfare that could redraw the map of the Middle East.

Mr. Netanyahu and other leaders continue to see Shiite Iran and its nuclear program as the primary threat to Israel, and Hezbollah as the most likely to draw it into direct battle. Still, the mounting strength of extremist Sunni cells in Syria, Iraq and beyond that are pledging to bring jihad to Jerusalem can hardly be ignored.