JERUSALEM — An Israeli laborer who was repairing the security fence along the border with Gaza was fatally shot on Tuesday by a Palestinian sniper, according to the Israeli military, and Israel immediately responded with airstrikes and tank and infantry fire against targets it associated with militant groups in the Palestinian coastal territory.

A Palestinian girl, Hala Abu Sbeikha, 3, was killed and at least four of her relatives were wounded when a shell landed in front of their home in the Maghazi refugee camp in the central part of Gaza, local hospital officials said.

The deaths were the latest in a growing wave of Israeli-Palestinian violence that is accompanying the difficult, American-brokered peace talks now underway. Prime Minister Benjamin Netanyahu of Israel had warned that the killing of the laborer would not go unanswered and that Israel would “respond with force.” He spoke during a visit earlier Tuesday to Sderot, the Israeli town about a mile from the Gaza border that has been subjected to Palestinian rocket fire for years.

Israel’s defense minister, Moshe Yaalon, said, “If there is no quiet in Israel, there will be no quiet in Gaza.”