At least five civilians were wounded, local medical officials said.
Their deaths come as violence continues to flare up between Israel and Gaza's rulers from the Islamic militant Hamas.
Streaks of light are pictured as rockets are launched from the northern Gaza Strip toward Israel, as seen from Sderot, Aug. 8, 2018.
The three flare-ups, which follow months of tensions due to protests and clashes along the Gaza border, have raised fears of a fourth war between the two sides since 2008.
The Hamas movement responded to Israeli airstrikes with rockets fired from Gaza towards southern Israel. A statement from the military wing of Hamas claimed responsibility for the rockets. Reports from Gaza stated that the family's home was adjacent to a Hamas target that Israeli forces attacked.
Israel's rescue service Magen David Adom said three Israelis, including two men ages 34 and 20, were taken to a hospital for treatment.
A number of terror targets in several military sites, including weapons and rockets, as well as a military compound that serves as a central logistic warehouse were also hit by IAF jets.
U.N. Middle East envoy Nickolay Mladenov said in an overnight statement: "I am deeply alarmed by the recent escalation of violence between Gaza and Israel, and particularly by today's multiple rockets fired towards communities in southern Israel".
A 30-year-old Hamas affiliate was killed in the strikes, the Gaza Health Ministry spokesman Ashraf al-Qedra said. Twelve others were injured, the Ministry said.More news: Meghan Markle’s Birthday Gifts: What She Can and Can’t Keep
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The mother and daughter died immediately and the father is in critical condition, Kamal said. In response, Israel responded with tank fire.
Israeli television broadcast images of a house and cars that were reportedly damaged by the rockets in Sderot.
The majority of the rockets hit open areas while four were intercepted, it said.
Israel has not commented on the reported casualties in Gaza yet.
The Gaza clashes reached their peak on May 14, marking the 70th anniversary of the Nakba Day (the Day of Catastrophe), which this year coincided with the USA embassy relocation from Tel Aviv to occupied Jerusalem al-Quds.
The UN, he said, has engaged with Egypt in an "unprecedented effort" to avoid serious conflict, but warned that "the situation can rapidly deteriorate with devastating consequences for all people".
Israeli media said officials were considering evacuating residents from areas near the Gaza border.
Neither the United Nations nor Egypt has publicly discussed its plans for a renewed Gaza cease-fire, but they said it would bring economic relief to Gaza's 2 million residents experiencing shortages under crippling blockades.
The demonstrations have been fueled in large part by pervasive despair caused by the blockade that has caused widespread economic hardship and left the coastal territory with crippling fuel shortages and just a few hours of electricity a day. Our strong commitment to the State of Israel's right to defend its borders and civilians is uncompromising.