Palestinians militants have also fired rockets into Israel and the Israeli military has carried out dozens of air strikes in the enclave.
However, earlier in the evening, at least two Israelis were injured as a result of rockets that landed in Sderot.
One Palestinian rocket hit a house, Israeli media said, showing footage of houses and cars pockmarked with shrapnel.
Sirens sounded in Israeli areas near Gaza, warning residents to seek immediate shelter, the Israeli army said.
It said the Palestinian "resistance" had fired a large number of projectiles at "enemy positions in the Gaza envelope".
Over the past four months, 158 Palestinians have been killed by Israeli fire, including at least 120 in the protests near the fence and others in Israeli air strikes and other incidents elsewhere in Gaza, according to the Gaza Health Ministry and a local rights group.
The Gaza Health Ministry say pregnant 23-year-old Enas Khammash and her 18-month daughter were killed in Jafarawi in central Gaza.
Streaks of light are pictured as rockets are launched from the northern Gaza Strip toward Israel, as seen from Sderot, Aug. 8, 2018.
The military said that it identified 36 rockets fired from Gaza at Israel and that the Iron Dome defense system intercepted several of them.More news: Dota 2 : 'Artificial intelligence' makes a record by defeating human players
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Parts of the town have been closed off and police bomb disposal units were at the scene of the strikes, a spokesman for the force said. A member of the Hamas' armed wing was also killed.
Jamie McGoldrick, the United Nations' humanitarian coordinator for the Palestinian territories, in a news release called Israel's restriction of fuel imports "a risky practice, with grave consequences on the rights of people in Gaza".
Gaza has been controlled by Hamas for more than a decade, during which time it has fought three wars against Israel, most recently in 2014.
The Israel Defense Forces Twitter account said its fighter jets had targeted more 140 strategic sites, including a weapons manufacturing and storage facility.
Clashes along the Gaza border since the end of March have seen at least 163 Palestinians killed by Israeli fire.
The escalation comes after the Hamas leadership convened for a rare meeting in Gaza on Friday.
United Nations and Egyptian-led efforts are under way to mediate a long-term truce between Israel and Hamas that would end a four-month surge of violence along the Israel-Gaza border.
Israeli forces have launched three military assaults on the Gaza Strip since 2008.
The truce, which is planned to last five years, would include the release of four Israelis: the remains of two fallen IDF soldiers and two living, mentally handicapped men who wondered across the Gaza border including two soldiers.