GAZA CITY, Gaza Strip — The Israeli military launched what could be a long-term offensive in the Hamas-ruled Gaza Strip on Tuesday, striking more than 100 sites and mobilizing troops for a possible ground invasion aimed at stopping a heavy barrage of rocket attacks against Israel.

At least 10 Palestinians, including two children, were killed in the attacks from air and sea, Palestinian officials said.

The military said the open-ended operation aims to deliver a blow against the Islamic Hamas group, and end the rocket fire that has reached deeper into Israel.

Israeli officials said the government had authorized the army to mobilize an additional 40,000 troops, if needed, for the operation. The army said there were no immediate plans to call up the troops but that they would be activated depending on operational needs. Israel has already mobilized about 1,500 reservists.

The rocket attacks and Israeli counterstrikes have intensified in recent weeks as tensions have soared over the killing of three Israeli teenagers and the apparent revenge killing of a Palestinian teenager by three Jewish suspects.

The military said more than 120 rockets hit Israel over the past two days, a dramatic spike after nearly two years of relative quiet that followed a previous Israeli campaign to root out Gaza rocket launchers.

Israel responded with dozens of airstrikes throughout Gaza, targeting the homes of several Hamas operatives allegedly involved in rocket fire.

In addition, the military said it struck militant compounds, concealed rocket launchers, and other militant infrastructure sites. Most were targeted by airstrikes, and three were attacked from the sea. Later, it also took out what it said was a Hamas command center embedded within a civilian building.

The four Hamas militants killed Tuesday died when an airstrike hit the car in which they were traveling, Hamas officials said. One of the dead was identified as Mohammed Shaban, a senior militant.

Later Tuesday, another airstrike hit the home of a Hamas leader in the southern town of Khan Younis, killing six people, Hamas officials said. They said two children were among the dead.