Israeli Prime Minister Benjamin Netanyahu on Sunday ordered the military to continue with "massive strikes" in Gaza, which have already killed 19 Palestinians.
Israel said it launched the strikes after rocket fire from the occupied territory killed three Israelis. The flare-up threatens a fragile truce mediated by Egypt and the UN.
At least 250 rockets have been fired into Israel from Gaza since Friday.
The Israeli military said many of the rockets were intercepted by its Iron Dome missile defence system, and it had moved an armoured brigade to the border with Gaza for "missions as needed".
Israeli forces said on Twitter they had destroyed 280 targets in Gaza.
Israel responded with more than 200 air strikes and tank fire, killing at least six Palestinians, including a baby and her pregnant aunt.
The family of 14-month-old Saba Abu Arar, and her aunt Falestine and her unborn child, say they were killed by an Israeli drone.
The Abu Arar family were gathered at a house in the Alzatoon neighbourhood in eastern Gaza at the time of the strike.
At the home, the baby's mother Rasha, 25, wailed "Seba is gone," repeatedly as a group of women tried to calm her down.
"Seba was with me, she was sitting in my lap when it hit us suddenly," Rasha told The National.
"I lost Seba and her sister is now in the hospital in the intensive care. I don't know anything about her."
Other relatives said the strike blew out the wall of the house, severely wounding Falestine, 37, who was the closest to the wall. She died later in hospital.
Seba's grandmother Mazoza, 70, was injured in her left thigh.
"I was sitting with my family outside my house. We were around 50 people. suddenly a 'bug' fell down where we were sitting and exploded," she said, using the Palestinian slang for an Israeli drone.
The strip, 40 kilometres long and 11km wide, is home to about two million people.
It is one of the most densely populated areas in the world and powerful strikes, even when precise, threaten civilian life.
Islamic Jihad, a smaller Gaza faction backed by Iran, said two of its fighters were killed in the strikes.
Mahmud Issa and Fawzy Bwadi were killed during an Israeli "bombardment in the central Gaza Strip", the group said.
Mr Netanyahu, also the Defence Minister, said on Sunday that he had ordered Israeli forces to attack militants in Gaza and station the infantry in strength around the Palestinian enclave after a two-day surge in fighting.
"This morning I instructed the Israel Defence Forces to continue with massive strikes against terrorists in the Gaza Strip and I also instructed that forces around the Gaza Strip be stepped up with tank, artillery and infantry forces," he said.
Mr Netanyahu held consultations with security chiefs before commenting on the flare-up.
One Israeli civilian was killed in a rocket strike on the southern city of Ashkelon near the Gaza border. Two more died in other rocket strikes on the city.
A factory in Ashkelon was hit directly by a rocket on Sunday afternoon, injuring three or four people inside, local media reported.
Islamic Jihad claimed responsibility for at least some of the rocket fire and said it was prepared for more.
Its armed wing distributed a video showing militants handling rockets and threatening key Israeli sites, including Ben Gurion Airport near Tel Aviv.
Turkish news agency Anadolu said its office building in Gaza was hit by at least five Israeli rockets.
"We strongly condemn Israel's attack," Anadolu said. "We call on national and international press organisations to react and take action regarding this violation of human rights and press freedom."
The latest violence began on Friday when an Islamic Jihad sniper fired at Israeli troops, wounding two soldiers. Israel retaliated with an air strike that killed two militants from Hamas.
Two other Palestinians protesting near the frontier were killed by Israeli forces on the same day, Palestinian officials said.
The escalation comes just before Ramadan and Israel's Independence Day holiday.
Israel is due to host the 2019 Eurovision song contest finals in less than two weeks in Tel Aviv.
Although aerial exchanges are frequent, Israel and Hamas have managed to avert all-out war for the past five years.
In the last conflict, which lasted seven weeks, more than 2,000 Palestinians were killed by an Israeli ground and air offensive known as Operation Protective Edge.
Egyptian and UN mediators, credited with brokering ceasefires in previous rounds of violence, were working to prevent further hostilities.
The ceasefire between Israel and Hamas had led to relative calm around Israel's April 9 general election.
But the past week saw a gradual rise in violence.
With the truce at risk, a Hamas delegation led by its Gaza leader Yahya Sinwar went to Cairo on Thursday for talks with Egyptian officials.
