Palestinian militants responded by launching a barrage of rockets towards Israel, prompting warning sirens to go off in Tel Aviv and in communities near the Gaza Strip.
Israeli Prime Minister Benjamin Netanyahu described Abu al-Ata as the "main terrorist instigator in the Gaza Strip."
"All terrorists think alike. They think they can harm civilians and hide behind civilians. We have proven that we can hit with surgical precision," he said at a press conference.
The Israel Defence Forces said Abu al-Ata was "directly responsible for hundreds of terror attacks against Israeli civilians and soldiers."
Mos'ab al-Briem, the spokesman of the Islamic Jihad militant group in Gaza, called the pre-dawn killing of its military leader an "assassination" and a "declaration of war against our Palestinian people."
Ahmad Helles, 30, a neighbour of the slain military leader, told dpa he had seen the bodies of Abu al-Ata and his wife on the road in front of their home.
Islamic Jihad is one of the most powerful militant groups in the Gaza Strip and has gained influence since 2014 with the help of financial backing from Iran.
Also on Tuesday, three Israeli rocket attacks west of the Syrian capital Damascus targeted the house of Akram al-Ajouri, who dpa sources said is another leader of the Quds Brigades.
Syrian state-run news agency SANA reported that the militant had not been killed in the attacks, but that his son, Mouaz, and another person were dead, and 10 other people were injured.
The Britain-based Syrian Observatory for Human Rights said al-Ajouri and his wife were among the wounded.
Two other Israeli airstrikes later on Tuesday killed two members of Islamic Jihad rocket-firing squads, one while riding a motorcycle in the northern Gaza Strip, the Israeli military and sources close to Islamic Jihad said.
The Palestinian Health Ministry confirmed a total of 10 dead - including Abu al-Ata and his 39-year-old wife Asma - as well as dozens injured in the Israeli airstrikes.
Gaza militants responded to the airstrikes by launching a wave of rockets into Israel.
The Israeli army said about 200 rockets had been fired, dozens of which were intercepted by the country's Iron Dome aerial defence system.
The Israeli Foreign Ministry said 40 people were injured in the attacks.
Israel's Magen David Adom (MDA) ambulance service said it had treated a total of 39 people.
The army posted an update on its Twitter feed saying that Israel had retaliated to the rocket attacks by targeting further Islamic Jihad sites.
One rocket fired from Gaza slammed into a major junction in southern Israel, narrowly missing two cars. One of the two drivers was taken to hospital with shrapnel wounds.
An 8-year-old Israeli girl suffered a cardiac arrest while running to a shelter in the southern Tel Aviv suburb of Holon, the MDA added.
A rocket also directly struck a house in Netivot and a factory in Sderot. Both towns are near the Gaza Strip.
Schools and kindergartens were closed and shelters opened in the greater Tel Aviv area, as two rockets were intercepted over the city.
In a press conference, Netanyahu called the Islamic Jihad military leader a "ticking time bomb" and said the targeted strike was unanimously approved 10 days ago by his security cabinet.
His military chief of staff, Aviv Kochavi, and the head of Israel's Shin Bet internal security organization, Nadav Argaman, said Abu al-Ata had been behind most of the attacks from Gaza over the past year, in violation of the informal ceasefire agreement between Israel and the Islamist Hamas movement, which rules the coastal strip.
Kochavi alluded to the fact that Israel was considering further targeted killings, saying: "If we have to, we will even return to the policy of targeted killings."
The United States government expressed its support for Israel.
"The Administration strongly condemns the barrage of rockets on Israeli civilians and continues to monitor the situation," tweeted Avi Berkowitz, an assistant to US President Donald Trump.
Berkowitz said the US backs its "partner and ally Israel in their fight against terrorism and the terrorist group, Palestinian Islamic Jihad."
The German government criticized the rocket attacks, saying: "There is no justification for violence against innocent people. ... Level-headedness and a sincere effort to achieve a de-escalation should have top priority in the current fragile situation."
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