JERUSALEM — The cross-border battle between the Israeli army and militants in the Gaza Strip stretched into a second day Wednesday, with dozens of rockets fired from Gaza following Israel’s targeted killing of a Palestinian Islamic Jihad leader a day before.

After an overnight lull, rocket fire began shortly before dawn, triggering renewed alarms in Israeli communities near the territory. Schools, banks and government offices in Gaza remained closed, and residents hunkered down as rockets and counterstrikes screamed overhead. In Israel, schools within 15 miles of Gaza were closed, keeping 300,000 students at home. Crossings into the territory remained shut.

The Israeli military said it struck rocket-launch sites in Gaza soon after the fusillade began, continuing strikes against purported Islamic Jihad military sites that have killed 26 people since Tuesday and injured more than 69, according to the Palestinian Ministry of Health. Israel said at least 20 of those killed were militants. The death toll also included three children, the ministry said.

The military said more 360 launches from Gaza into Israeli territory had been detected. The country’s air defense system, Iron Dome, intercepted dozens of rockets, and most others fell into open areas. But several homes, business and roadways were hit. Israel reported no fatalities but many minor injuries, mostly from the scramble of thousands of people to shelters when the alarms sounded.

The Israel Defense Forces said it was continuing its strategy of hitting assets controlled by the Islamic Jihad, an Iranian-backed militant group that Israel blames for a string of recent terrorist attacks. Officials were cautiously optimistic that Hamas, the militant group with governing authority in Gaza, would stay out of the fight.

That still seemed to be the case Wednesday, according to Lt. Col. Jonathan Conricus, an Israeli military spokesman.

The most intense fighting around Gaza in months began early Tuesday when Israel launched a lethal airstrike at the house of Baha Abu al-Ata, the Islamic Jihad commander in northern Gaza whom Israel considered responsible for several previous rocket attacks. At least one missile fired by a fighter jet struck the top floor of Abu al-Ata’s home, killing him and his wife. The Israeli army said his wife was not an intended target.

Officials said they were justified in the targeted killing because Abu al-Ata, characterized by Prime Minister Benjamin Netanyahu as the “chief terrorist in Gaza,” was preparing to carry out further attacks on Israeli citizens.

The security establishment had come to consider Islamic Jihad a greater threat emanating from Gaza than Hamas, which itself has struggled with the destabilizing influence of the extremist group. Israel would not comment on a second airstrike early Tuesday that hit the home of another Islamic Jihad commander in Syria, an attack that was also widely believed to be the work of Israeli forces.

In Gaza, residents took cover amid explosions that seemed to come from all over, with Israeli air and tank strikes, Iron Dome intercepts and the rocket launches, not all of which cleared the territory before exploding.

Most streets were quiet, and many grocery stores and bakeries remained closed Wednesday. Gazans, who have suffered multiple wars between the militants in their midst and Israeli forces beyond the border, are already struggling under a moribund economy and grinding unemployment.

“We are in constant concern, there is no human life in Gaza, and now the conditions are getting more complicated,” said Samira Arafat, 52, who was walking empty streets to find bread and vegetables. “Me, my husband and my children slept in one room last night, fearing the sounds of shelling and rockets.

“People in their homes are waiting for what will happen in fear and pain,” she added.

For Mohammed Kahlout, 39, who was standing at the door of his house with two of his neighbors, the fighting brings fear, but also the notice of a world that he thinks has forgotten Gaza.

“Whether there is bombing or not, there is no work, there are no basic services, electricity is cut,” he said. “I don't care whether there is war or not. At least the world looks at us and follows our news when there is escalation.”

Naftali Bennett, Israel’s new defense minister, who took up the post hours after Abu al-Ata’s assassination, said in a statement Wednesday that the operation was “vital for Israel’s security.”

“Baha Abu al-Ata was a terrorist architect of Islamic Jihad who worked against Israeli citizens, and he was eliminated,” said Bennett, who has been at odds with Netanyahu in the past over taking a harder stance when dealing with militant elements in Gaza. “We did it yesterday and will not hesitate to act in the future. We send a clear message to all our enemies: Whoever plans to hurt us during the day will not make it through the night.”

Both Hamas and Islamic Jihad are designated as terrorist organizations by international bodies. Israel has urged Hamas to contain the smaller group, which is considered more determined to launch attacks.

Israel said it holds Abu al-Ata in particular responsible for numerous rocket attacks over the past few years, including one in early September that sent Netanyahu rushing for cover during a public event in Ashdod while he was on the election campaign trail.

Many consider Tuesday’s assassination directly connected to that attack. But members of the Israeli cabinet said Abu al-Ata was targeted because his activities undermined the uneasy truce between Israel and Hamas.

In previous flare-ups, Israeli policy was to retaliate against Hamas, holding the group responsible as the ruling body in Gaza. In this cycle, the army appears to be targeting Islamic Jihad’s infrastructure, including rocket-launching sites above and below ground, delivering a blow to the militant group that is the second-largest in the strip.

Gilad Erdan, the minister of strategic affairs, said that Israel still holds Hamas responsible for all violence emanating from the territory, but he confirmed that the focus is on Islamic Jihad for now.

“If Hamas continues to allow [Palestinian Islamic Jihad] to fire or joins in, then we will target them, too,” he said.

Balousha reported from Gaza.