Islamic Jihad vowed to "avenge" the deaths in the pre-dawn raid involving some 40 Israeli aircraft which hit targets in the crowded coastal enclave for nearly two hours from just after 2:00 am (Monday 2300 GMT).
The Gaza health ministry said four children were among those killed and 20 people were wounded, some of them in serious or critical condition, in the attacks which left buildings ablaze and reduced others to rubble.
Later, violence flared in the occupied West Bank when Israeli forces launched a raid in Nablus in which at least a dozen people suffered bullet wounds, according to Palestinian medics.
The Israeli army said that in its Gaza strikes it had targeted three leaders of Islamic Jihad, which it considers a terrorist group, as well as its "weapon manufacturing sites".
Asked about child casualties, army spokesman Richard Hecht said: "If there were some tragic deaths, we'll look into it."
Islamic Jihad confirmed three of its senior members were killed in Gaza.
It named them as Jihad Ghannam, secretary of the Al-Quds Brigades military council, Khalil al-Bahtini, commander of the military wing in northern Gaza, and Tareq Ezzedine, a military leader in the West Bank who operated from Gaza.
AFP photographers saw the body of a man identified as Ghannam in Rafah, in the south of the Gaza Strip, and also a boy's body in the morgue of Gaza City's Shifa hospital, where mourners had gathered.
Islamic Jihad vowed to retaliate, with spokesman Daoud Shehab warning that "the resistance considers that all cities and settlements in the Zionist (Israeli) depths will be under its fire".
Hecht said the military was "looking where this thing will develop", while instructing Israeli residents within 40 kilometres (25 miles) of the Gaza border to stay near bomb shelters until Wednesday evening.
- 'Avenge the leaders' -
Israel last week traded air strikes on Gaza for rocket fire from the enclave, an exchange sparked by the death in Israeli custody of a Palestinian hunger striker with ties to Islamic Jihad, which ended with an Egypt-brokered truce.
Islamic Jihad charged on Tuesday that Israel had "scorned all the initiatives of mediators" and vowed it would "avenge the leaders" killed in the latest air strikes.
"It's about time!" Israeli National Security Minister Itamar Ben-Gvir wrote on Facebook, after criticising what he perceived as the military's weak response to Gaza militants last week.
The Israeli military described Ghannan as "one of the most senior members" of Islamic Jihad who had coordinated weapons and money transfers with Hamas.
Bahtini was "responsible for the rocket fire toward Israel in the past month", Israel said.
And Ezzedine, who was released from Israeli detention in a 2011 prisoner exchange, had been planning "multiple attacks against Israeli" civilians in the West Bank, it charged.
An Islamic Jihad source told AFP that Ezzedine was part of a delegation from the group that had been due to travel to Cairo for a meeting Thursday, which has now been cancelled.
- 'Treacherous operation' -
later Tuesday, Israeli forces raided central Nablus in the West Bank, which has been occupied by Israel since the Six-Day War of 1967, sparking clashes as they detained two people.
The Palestinian Red Crescent Society said its medics treated 145 injuries in Nablus, including a dozen people who were shot with live fire and many more who suffered tear gas inhalation.
Israeli forces initially shot at people throwing rocks at them, an army statement said, before troops came under live fire as they withdrew from the Palestinian city.
Hamas chief Ismail Haniyeh said in a statement on the Gaza attacks that "assassinating the leadership in a treacherous operation will not bring security to the occupier, but instead greater resistance".
Following the air strikes, Egypt stated its "total rejection of such attacks" which "inflame the situation in a way that could get out of control in the occupied Palestinian territories."
Israel and Gaza militants have fought multiple wars since Hamas took control of the enclave in 2007.
A three-day conflict in Gaza last August left 49 Palestinians and no Israelis dead, with Cairo playing a key role in securing a ceasefire.
Tuesday's deaths bring to 121 the number of Palestinians killed in the Israeli-Palestinian conflict so far this year.
Nineteen Israelis, one Ukrainian and one Italian have been killed over the same period, according to an AFP count based on official sources from the two sides.
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