Israel said it had launched an operation targeting militants who posed an imminent threat to its citizens.
Islamic Jihad has vowed revenge and Gaza-based militants are expected to respond with rocket fire into Israel.
The extent of any escalation is likely to depend on whether Hamas, which controls Gaza, decides to join in.
Israel officials are said to be preparing for days of fighting.
The strikes were the deadliest since three days of hostilities between Israel and Islamic Jihad last August, in which 49 Palestinians were killed in Gaza.
Dentist Dr Jamal Khaswan's family lived in the top floor of a Gaza City apartment building that was targeted
The latest strikes took place in the early hours of Tuesday morning, when 40 Israeli warplanes and helicopters attacked in several waves across Gaza, hitting homes and causing panic among residents.
Pictures showed at least two apartments with their fronts ripped away and others damaged.
The Gaza health ministry said four children and four women were among those killed. Half of the injured were women and children and several were in a critical condition in hospital, it added.
Russia's representative office in the Palestinian territories announced that one of its citizens, Dr Jamal Khaswan, a former chairman of the Gaza Dentists' Association, was killed along with his wife Mervat and their 21-year-old son Youssef.
Another two of their children survived, it said. They included 10-year-old daughter Diala, who was filmed sitting in the front seat of an ambulance and crying out for her father.
Dr Wafai al-Sousi, a friend and colleague of Dr Khaswan, condemned what he called the "cowardly targeting" of the family.
"I was very surprised. He was just an incredible doctor... with a good reputation. He did not belong to any political party and never worked with any military entity," he told the BBC.
Palestinian sources said Dr Khaswan lived in an apartment in Gaza City close to one of the militants who was killed.
Islamic Jihad's military wing, the al-Quds Brigades, confirmed the deaths of three of its commanders, along with their wives and a number of their children. It identified them as:
- Jihad Shaker al-Ghannam, secretary of the al-Quds Brigades' Military Council
- Khalil Salah al-Bahtini, the commander of its Northern Region
- Tariq Mohammed Ezzedine, "one of the heads of military action" in the occupied West Bank
"We affirm that the blood of the martyrs will increase our resolve," the al-Quds Brigades said. "We will not leave our positions, and the resistance will continue, God willing."
Large crowds of mourners turned out for the funerals after midday prayers.
On Tuesday afternoon, the Israel Defense Forces (IDF) said one of its aircraft struck a "terrorist squad" carrying anti-tank guided missiles towards a firing position in Khan Younis, in southern Gaza.
The Gaza health ministry said two people were killed and two others injured.
Israel said Jihad Ghannam, Tariq Ezzedine and Khalil al-Bahtini were responsible for recent attacks
Israel's Defence Minister, Yoav Gallant, said its forces "precisely carried out their mission against the leadership of the Islamic Jihad in the Gaza Strip".
"Any terrorist who harms Israeli citizens will be made to regret it."
The IDF said Bahtini was the senior operational officer of Islamic Jihad in Gaza, and that he was responsible for the rocket fire from Gaza in the last month.
"He was an imminent threat to the security of Israeli civilians."
It added that Ghannam was a senior member of Islamic Jihad's rocket force and that Ezzedine was in charge of co-ordination with the group's operatives in the West Bank and planning attacks on Israeli civilians there.
The IDF said its aircraft also struck 10 sites used to manufacture weapons and six Islamic Jihad military facilities.
Spokesman Lt Col Richard Hecht said the operation had "achieved what we wanted to achieve", according to AFP news agency.
When asked about child casualties, he replied: "If there were some tragic deaths, we'll look into it."
He also said residents of Israeli communities within 40km (25 miles) of Gaza had been advised to stay close to bomb shelters until Wednesday evening.
Mr Gallant warned council leaders and officials in southern Israel that they "must be ready for any scenario, including a prolonged campaign and expanding the firing ranges" of rockets from Gaza.
Officially known as Palestinian Islamic Jihad (PIJ), the militant group is the biggest in Gaza next to Hamas.
It has been responsible for many of the rocket attacks on Israel from the territory in recent years and is sworn to Israel's destruction.
There was a serious flare-up last week, as Islamic Jihad and other groups fired several barrages of rockets into Israel over two days following the death in an Israeli prison of a Palestinian hunger striker. The Israeli military carried out air strikes in response.
Armed groups in Gaza said those responsible for the strikes should "prepare to pay the price"
Hamas leader Ismail Haniyeh warned: "Assassination of leaders will not bring the Occupation [Israel] security but more resistance."
An umbrella of militant groups groups in Gaza said in a statement they would mourn all those who died as a result of what they called "the treacherous Israeli aggression" and that those responsible should "prepare to pay the price".
The spokesman for West Bank-based Palestinian President Mahmoud Abbas, Nabil Abu Rudeineh, said the Israeli government "bears full responsibility for this dangerous escalation".
UN Middle East envoy Tor Wennesland condemned the deaths of civilians and urged all parties to exercise maximum restraint.
"I remain fully engaged with all sides in an attempt to avoid a broader conflict with devastating consequences for all," he said.
Hours after the strikes on Gaza, Israeli forces carried out a raid in the northern West Bank city of Nablus.
Palestinian news agency Wafa reported that two Palestinians were detained and that 13 others were shot and injured during confrontations with the Israeli troops. Israeli media meanwhile said a soldier was lightly injured when a bomb exploded beside an armoured vehicle in which he was travelling.