Hamas, the Islamic militant group that governs here, fired barrages of rockets into southern Israel on Tuesday after a break of more than a year during which the group largely adhered to an informal cease-fire.

By evening, Israel had issued a stern warning that it was examining all possible responses, signaling the potential for a sharp escalation in the area.

The rockets were apparently a reaction to three Israeli airstrikes here on Monday and Tuesday that killed six Palestinians, most of them militants. The Israeli military said it had attacked terrorist squads responsible for firing rockets and for sniper fire along the border with Israel.

A Palestinian toddler, 2, was killed and her older brother was injured Tuesday evening in a blast at their house, witnesses and medical officials said. Residents said an Israeli plane had fired a missile at the house, in the Zeitoun neighborhood in Gaza City, but the Israeli military said that it did not carry out strikes at that time and that an initial investigation had indicated that the blast was caused by a failed rocket launching from inside Gaza.

More than 45 rockets had landed in Israeli territory by Tuesday evening. Most fell in open areas. But one hit a building in an Israeli police base at a communal farm near the border, wounding two officers, a police spokesman said. Israel’s defense minister, Ehud Barak, was holding consultations with the top echelons of the military and intelligence branches and was examining “a whole range of possible responses,” his office said in a statement.

Hamas has kept out of the last few rounds of violence, leaving smaller, more radical groups like Islamic Jihad to fire rockets and then restraining them in an effort to restore calm, often with the help of Egyptian mediators.

But there was a sense that Islamic Jihad was gaining ground, while the smaller groups and many residents here criticized Hamas for not avenging the Israeli strikes. Hamas, whose name is an acronym in Arabic for the Islamic Resistance Movement, was being accused of having abandoned the path of resistance against Israel.

Such factors may have influenced Hamas to change direction on Tuesday, a decision that came against a background of broader regional shifts and turmoil.

“Hamas has given a chance to efforts by Egypt and other sides to stop and prevent the Israeli aggression,” Fawzi Barhoum, a Hamas spokesman here, said by telephone, “but Israel did not respect any of them. Keeping silent makes no sense.”

Waleed al-Modallal, a political scientist at the Islamic University of Gaza, said Hamas had emerged from recent internal elections “stronger and more organized” at a time of regional change, and that it had been buoyed by the rise of Islamic political power in Egypt and other areas.

There was also some internal pressure from Hamas supporters calling on the movement “not to leave the battlefield and to carry out its role alongside the other factions,” Mr. Modallal said in a telephone interview.

Hamas said it had aimed its rockets at a civilian community and an Israeli military base near the border. In anticipation of Israeli military action, Hamas security forces evacuated their bases and headquarters here.

The latest flare-up over the border came after an attack on Monday by militants along the border with Egypt that killed an Israeli construction worker.

A group that apparently has a jihadist bent calling itself the Shura Council of the Mujahedeen in Beit al-Maqdes (Beit al-Maqdes means Jerusalem) released a video on Tuesday claiming responsibility for the attack along the Egyptian border.

The Israeli military said two of the assailants were killed in an ensuing clash with Israeli forces when Israeli gunfire detonated explosives carried on one of their bodies. The video presented two men who it said were on a suicide mission. It said one was a citizen of Saudi Arabia and the other an Egyptian citizen.