The raids underline how al-Qaida, which is also attacking the Jewish state from Egypt's Sinai Peninsula, is now deemed a threat to Israel amid the political upheavals across the Arab world throughout 2011 that have propelled radical Islamist parties into power.
This is seen as a potentially major boost for the jihadists and could have enormous political impact in the volatile region by ending the power of Arab dictators friendly with the United States.
"What's happening in Sinai is that global terrorist organizations are meddling there and their presence is increasing because of the connection between Sinai and Gaza," Israel Prime Minister Binyamin Netanyahu warned recently.
Alarm was heightened by Western intelligence reports senior al-Qaida veterans are moving from Pakistan and Afghanistan to North Africa, possibly to exploit the political turmoil there.
Al-Qaida has had affiliates operating in Gaza for some time but these have come to prominence since the fundamentalist Hamas movement seized control of the strip in 2007 from the mainstream Fatah organization.
Hamas has sought to crush the jihadists who challenged its authority but there are at least four jihadist groups operating in the coastal territory. These have taken to mounting rocket and infiltration attacks on Israel, seeking to provoke Israeli retaliation and block reconciliation between Hamas and Fatah that could bolster the moribund peace process.
In the airstrikes that began Dec. 27 following rocket attacks from Gaza, the Israelis killed several al-Qaida operatives, who the military calls "global jihad-affiliated terrorists."
Two of those slain, identified as Ramo Daoud Jabar Khafarna and Hazam Saadi al-Shakr, were former members of Hamas who defected to the Salafists. Another was Muaman Abu Daf, reputedly a leader of Jaish al-Islam, or Army of Islam, one of the main jihadist groups.
The Israelis claim the fourth fatality, Abdallah Telbani, had taken part in rocket and bombing operations against Israel in Gaza and the Sinai.
There are four key Salafist groups in Gaza that have proclaimed loyalty to al-Qaida.
These are Jaish al-Islam; Jund Ansar Allah, or Warriors of God; Jaish al-Ummah, or Army of the Nation; and Jaish al-Muminun, or Army of Believers, also known as al-Qaida in Palestine.
At the same time, there have been persistent reports al-Qaida operatives are infiltrating Lebanon, on Israel's northern border, to foment unrest there as the regime in neighboring Syria battles a stubborn pro-democracy uprising there aimed at toppling President Bashar Assad.
Lebanese Prime Minister Najib Mikati has denied that but pro-Syrian Defense Minister Fayez Ghosn says the jihadists are infiltrating Lebanon posing as Syrian opposition activists aiming to destabilize the country.
Syria's opponents in Lebanon claim the beleaguered Damascus regime seeks to whip up sectarian violence in Lebanon to block support there for the anti-Assad uprising in which by U.N. count 5,000 people have been killed since March 15.
Al-Qaida has had a presence in Lebanon, which is still technically at war with Israel, for several years.
In 2007, the army fought a 300-strong jihadist group known as Fatah al-Islam, which included scores of Saudi Arabians, in a Palestinian refugee camp in northern Lebanon for five months before crushing them.
Hundreds of people were killed but Fatah al-Islam was never completely eradicated.
Al-Qaida has operatives in the volatile Ain al-Hilweh camp outside the southern port city of Sidon and is widely perceived to be spreading.
But for now, Gaza seems to be the main flash point for the Israelis, although it's more likely the vast Sinai Peninsula, mostly desert and mountains, will become a greater threat as al-Qaida builds its strength there while Cairo's control dwindles.
An Aug. 18 attack in which eight Israelis and five Egyptian troops were killed in the southern Sinai and the repeated bombing of the Egypt-Israel natural gas pipeline underline the danger.
The Egypt-based jihadists announced the formation of their Sinai wing, Ansar al-Jihad in the Sinai Peninsula, in December. Israel is bracing for trouble.
Notable deaths of 2014 [PHOTOS]