Islamic Jihad vowed to "avenge" the deaths in the raid involving some 40 Israeli aircraft, which hit targets in the crowded coastal territory for nearly two hours from just after 2:00 am (2300 GMT Monday).
The Gaza health ministry said four children were among those killed and 20 people were wounded, with some in critical condition, in the attacks which left buildings ablaze and reduced others to rubble.
The Israeli army said 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 the deaths of three senior members -- Jihad Ghannam, Khalil al-Bahtini and Tareq Ezzedine -- before their bodies were later carried through the streets in mass funeral processions.
The group 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".
Hamas chief Ismail Haniyeh said in a statement that "assassinating the leadership in a treacherous operation will not bring security to the occupier, but instead greater resistance".
The Israeli military warned residents within 40 kilometres (25 miles) of the Gaza border to stay near bomb shelters until Wednesday evening.
Moscow's diplomatic mission to the Palestinians said one of the dead was a Russian citizen, a doctor who was killed alongside his wife and one of his children.
- '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.
Defence Minister Yoav Gallant labelled Tuesday's strikes a "precise operation" and warned that Israel "will not tolerate rocket fire, terrorism or any threats to the sovereignty of our state and security of our citizens".
"It's about time!" Israel's far-right 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.
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.
The group said Ghannam was secretary of the Al-Quds Brigades military council, Bahtini the military commander in northern Gaza, and Ezzedine a military leader in the West Bank who operated from Gaza.
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", the army 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' -
The United Nations' Middle East peace envoy, Tor Wennesland, said he was "deeply alarmed" by the latest violence and described the killing of civilians as "unacceptable".
Jordan's foreign ministry spokesman, Sinan Majali, said Amman was taking steps to "immediately stop this dangerous escalation".
Israel told a UN meeting in Geneva it was justified in carrying out what it labelled Operation Shield and Arrow, which it said followed "months of attacks against Israeli citizens".
"Israel directs these attacks only against military targets and takes all feasible precautions to mitigate harm to civilians," Avishai Kaplan, with the military's International Law Department, told the UN Human Rights Council.
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.
Following Tuesday's air strikes, Egypt's foreign ministry stated its "total rejection of such attacks" which it said "inflame the situation in a way that could get out of control in the occupied Palestinian territories."
The Gaza 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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