TEL AVIV — Despite a pledged cease-fire agreement between Hamas and Israel, attacks escalated on both sides of the Gaza border on Saturday, killing at least three Palestinian men and a 6-year-old boy in Gaza, and wounding an Israeli man in Sderot, officials said.

Ayman Taha, a spokesman for the Hamas government, which rules Gaza, said Saturday night that the Egyptian-brokered agreement, reached on Thursday, did not specify “a certain hour for the cease-fire to take effect.”

“We will be committed to the cease-fire as long as Israel does,” he said by telephone. “When Israel stops its aggression, our responses to it will stop as well.”

Spokesmen for the Israel Defense Forces and for Prime Minister Benjamin Netanyahu would not discuss the cease-fire. But as two dozen rockets rained down on the weary neighborhoods near Gaza City, the Israeli military chief, Lt. Gen. Benny Gantz, called a rare Sabbath meeting of top aides to “determine the next course of action,” according to a military spokeswoman.

Mr. Netanyahu, meanwhile, was briefed by General Gantz and Defense Minister Ehud Barak, and told them “to do what needs to be done to protect Israel’s population,” a senior aide said.

The renewed fighting comes just after the fifth anniversary of Hamas’s taking full control of the Gaza Strip, and amid an internal struggle for leadership. Until last week, Hamas had largely adhered to an informal cease-fire for more than a year, although militant Palestinian factions had frequently fired rockets into southern Israel. The latest flare-up began Monday with the killing of an Israeli construction worker building a fence along the border with Egypt, and attacks continued over the next two days.

Tensions had cooled by Thursday but picked up early Saturday morning, when Israel struck two Hamas sites in the northern Gaza Strip and one in the south. In the afternoon, the military spokeswoman said, two suspected terrorists “about to launch rockets at Israel” were directly targeted in separate attacks.

Palestinian officials said the first attack, around 1:30 p.m., killed Khaled al-Buri, who was affiliated with the Popular Resistance Committees, a group loyal to Hamas that claimed responsibility for firing dozens of rockets and missiles into Israel in recent days. The second, at 5 p.m., was apparently aimed at a motorbike rider in Gaza City. But witnesses said he escaped unharmed, while the rocket hit an apartment building, sending bricks onto the street that killed Osama Ali, 42, and wounded 10 others.

And Saturday morning in the southern Gaza town of Khan Yunis, witnesses said, an Israeli artillery shell killed Ali al-Shawaf, 6, and wounded his father, who died later in the day. “The boy and his father were sitting on the street outside a soccer court when the shells landed,” said Ahmed Arafat, 20, a witness.

Lt. Col. Avital Leibovich of the Israeli military said on Twitter that the boy had died in an explosion of Palestinian ordnance.

Israeli military officials said 24 rockets fired from Gaza hit southern Israel on Saturday, part of a weeklong barrage of more than 150; 10 were intercepted.

A school and factory were among the sites hit, and officials urged residents to stay indoors. Jodi Rudoren reported from Tel Aviv, and Fares Akram from Gaza. (Copyright 2012 The New York Times Company 06/24/12)