A breakdown in ceasefire talks has led to a flare-up in hostilities, with Israel retaliating after two of its soldiers were wounded by gunfire from an Islamic Jihad sniper on Friday.
This weekend, Palestinian militants have fired a wave of rockets into southern Israel, which has responded with “massive” airstrikes.
At least nine Palestinians, including the pregnant mother and her niece, and three Israelis have been killed since Saturday in some of the bloodiest fighting following the weeks-long 2014 war.
Gaza’s health ministry said the pregnant woman, 37, was severely wounded in an Israeli airstrike that hit a home in east Gaza City, and died later in hospital.
The 14-month-old girl, Seba Abu Arar, was killed in the strike, it said.
But the Israeli military said the pair had died due to a misfiring Palestinian rocket.
Israel said it has been targeted by more than 500 rockets since Saturday and many had been intercepted by its Iron Dome anti-missile system.
In Gaza, at least four Palestinian gunmen were killed in Israeli airstrikes, according to health officials.
In a separate strike, Hamas commander Hamed Ahmed al Khodary was killed when his car was hit in what Israel’s military called a targeted attack.
Meanwhile in Israel, police said a 58-year-old Israeli father-of-four, Moshe Agadi, was killed when a rocket hit a house in Ashkelon, about six miles north of Gaza, causing damage to several other buildings.
He was the first Israeli civilian fatality since the seven-week-long Gaza war in 2014. Separate strikes on the southern Israeli city killed two men.
Israeli Prime Minister Benjamin Netanyahu says he has ordered Israeli forces to attack militants in the Gaza Strip.
“This morning I instructed the IDF (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,” said Mr Netanyahu, who doubles as Israeli defence minister.
Iran’s foreign ministry has condemned what it called Israel’s “savage” attack on Gaza, and blamed “unlimited US support” for Israel.
Israel and Hamas, an Islamic group which rules Gaza and opposes Israel’s existence, have fought three wars and dozens of smaller flare-ups since Hamas seized control of the territory in 2007.
They fought for several days in March before Egypt brokered a truce in which Israel agreed to ease a crippling blockade on Gaza in exchange for a halt in rocket fire.
The latest fighting came as leaders from Hamas and Iran-backed armed faction Islamic Jihad were in Cairo for talks with Egyptian mediators aimed at preventing the cease-fire from collapsing completely.
Mr Netanyahu has said Hamas is not only responsible for its own militant actions but also those of Islamic Jihad group, which operates in the Gaza Strip.