The Israeli military and Palestinian militants in Gaza exchanged more fire on Saturday morning, as the biggest conflagration in the strip for a year moved into a second day.

Israel targeted what it said were rocket factories and depots belonging to Islamic Jihad, the second-largest militant group in Gaza, after Hamas, while Palestinian militants fired rockets and mortar over Israeli towns closest to the edge of the territory.

News media reports showed images of two residential buildings being flattened by Israeli missile strikes. The Israeli military said its helicopters and vessels had targeted what it described as two weapons storage facilities, which it said were located “in the residences of terrorist operatives in the Islamic Jihad terrorist organization in the Gaza Strip.” It was unclear whether they were referring to the same residential buildings.

Part of a rocket fired out of Gaza hit a house in the Israeli border town of Sderot, the Israeli police said. The inhabitants of the house escaped uninjured.

One Palestinian was killed in the overnight strikes, according to the Health Ministry in Gaza, bringing the total Palestinian death toll to 11, including a 5-year-old girl, while two Israelis were injured while seeking shelter on Friday.

Most of the projectiles that entered Israeli territory appeared to have been intercepted by Israel’s Iron Dome air defense system or to have fallen in open areas, although one rocket struck an Israeli community near the Gaza border on Saturday morning, slightly injuring one civilian, according to Israeli media reports. By midday, sirens warning of incoming rocket fire were sounding farther north, in the Israeli port city of Ashdod.

No cease-fire appeared imminent, despite early mediation efforts by international actors, including the United Nations. Ismail Haniyeh, the leader of the political bureau of Hamas, the main Islamic militant group in Gaza, said that he had spoken overnight with officials from Egypt and Qatar, as well as with the United Nations.

The battle began Friday afternoon when Israel launched airstrikes that it said were a pre-emptive attempt to foil an imminent attack from Gaza by Islamic Jihad, after almost a week of rising tensions between Israel and the militant group.

Israel arrested one of the group’s senior commanders this week in the West Bank, leading to threats of reprisal from its Gaza leadership, before an Israeli airstrike on Friday that killed Taysir al-Jabari, a senior leader of the Al-Quds Brigades, the armed wing of Islamic Jihad.

On Saturday morning, an Israeli military spokesman, Ran Kochav, told Israeli public radio that the fighting would most likely last for at least a week and that no negotiations were underway.

But overnight, the militants reduced the range of their rocket fire, aiming mostly at areas close to Gaza instead of cities farther to the north, which they initially targeted.

Analysts said that recalibration could prevent the situation from escalating further — as could a decision by Hamas to remain on the sidelines of the fighting.

Islamic Jihad is a second, smaller Gaza-based militia that sometimes acts independently of Hamas, which does not always support the secondary group in its rocket wars with Israel, most notably in 2019.

Israeli officials have said that they are targeting only Islamic Jihad, after they said the latter had been on the verge of firing anti-tank missiles at Israeli targets on Friday afternoon.

To underscore that point, the Israeli military also announced that it had arrested 19 Islamic Jihad operatives in raids overnight across the occupied West Bank.

Israel also closed public beaches along the coastline north of Gaza, anticipating further rocket fire there.