Twenty-two Palestinians, including two pregnant women, were confirmed dead by Gaza authorities as a result of the flare-up with Israel.
The Israeli military said it struck 320 Hamas and Islamic Jihad targets in Gaza on Sunday in retaliation for 600 rockets launched from the Strip that have killed four Israelis.
Aircraft have been striking Hamas' public security headquarters, the military said. Other targets included underground tunnels, military compounds, a weapons production facility, and rocket launch sites.
Islamic Jihad has said seven of the dead were members of the group. The Gaza Health Ministry said 146 wounded people have been taken to hospitals.
A Hamas operative in charge of Iranian fund transfers was killed in a joint operation by the military and Shin Bet security service, the army said.
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Hamas later confirmed Hamed al-Khoudary was a senior official in the organization. This is the first targeted assassination since 2014.
The Israeli army later said it struck another militant in the southern Gaza Strip.
The Gaza Health Ministry named others who were killed as Imad Muhammad Nasir, 22; Saba Mahmoud Abu Ar'ar, a year and a half, her aunt, Falestine Saleh Abu A'rar and the unborn fetus the latter was carrying; Khaled Mohammad Abu Qliq, 25; Mahmoud Subhi Isa, 26; Fawzi Abrd El-Hamid Bwadi, 24.
Israel's army attributed the death of the pregnant woman and her infant niece to a Hamas explosive, refuting Palestinian claims that they were killed by Israeli airstrikes.
The security cabinet convened earlier Sunday and has instructed the military to expand its attacks and to bolster reinforcements near the Gaza Strip, as consultations are ongoing.
The conflict between Israel and Gaza factions entered its second day Sunday, after a night that saw the first Israeli fatality.
A 58-year-old Israeli man was killed after a rocket hit his mother-in-law's home in the southern city of Ashkelon overnight Saturday, leaving behind a wife and four children. Three more Israelis were killed in a separate rocket strike later Sunday, at a factory in Ashkelon.