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Trying to claim a middle ground, Hamas leaders issued fiery statements Sunday in support of those firing rockets, but Gaza Prime Minister Ismail Haniyeh also noted that “the brothers in Egypt are working around the clock to stop the (Israeli) aggression.”

The United States and the United Nations called on both sides to show restraint.

Israeli airstrikes Sunday killed a 12-year-old boy, a 60-year-old farm guard and a militant, said Gaza health official Adham Abu Salmia. The boy was hit while walking with a friend to school in the northern town of Jebaliya, and the guard died in Gaza City while walking with his dog, which also was killed, he said. The militant was killed at a rocket launching site, he said.

Hundreds of mourners attended funerals in two Gaza towns Sunday. Women wailed and men chanted slogans demanding revenge for the deaths as militants fired guns into the air. The boy’s body was draped in the black flag of the Islamic Jihad militant group.

On Sunday, Palestinians fired more than 30 rockets at southern Israel. One struck the courtyard of an empty school in Beersheba, police said. Sunday is a school day in Israel, but schools in rocket range were closed to try to prevent casualties.

Three Israelis have been hurt by rocket fire since Friday, two of them seriously, the Defense Ministry said.

Israel claimed success in the first major battlefield test of its of its Iron Dome anti-missile system, which intercepted 30 of more than 120 rockets fired from Gaza since Friday, Mr. Barak told Israel’s weekly Cabinet meeting, according to a statement from his office. He said anti-rocket batteries were deployed near three southern cities close to Gaza.

Karin Laub reported from Ramallah, West Bank. Associated Press writer Aron Heller in Jerusalem contributed to this article.