JERUSALEM — Palestinian militants launched about 250 rockets and mortar shells into southern Israel from Gaza on Saturday, and the Israeli military responded with airstrikes and tank fire against targets across the Palestinian territory, as tensions along the volatile border boiled over and a fragile cease-fire faltered again.

Four Palestinians — including one militant, another man, a pregnant woman and her young daughter — were killed in Israeli strikes on Saturday, according to Gaza Health Ministry officials. That would bring the total number of Gazans fatally struck by Israeli fire since Friday to eight.

But on Sunday morning, the Israeli military’s chief spokesman, Brig. Gen. Ronen Manelis, said on Twitter that the mother and daughter were killed in a Hamas misfire, not from an Israeli strike.

The fighting also claimed the life of an Israeli man in the city of Ashkelon who was killed after a rocket launched from Gaza hit a house, the Israeli police said. In addition, one Israeli woman was severely wounded by shrapnel, according to Israel’s emergency services, as Gaza militant groups broadened their range of fire on Saturday afternoon, striking Kiryat Gat, an Israeli city about 20 miles northeast of the Palestinian enclave.