The Israeli military, on Twitter, said Hamas "uses Palestinians as human shields when firing rockets at Israel." The tweet included a photo of what Israel said showed Hamas "caught firing a rocket" from a civilian area.

Israeli warnings: Stay away from Hamas

A CNN producer was among those who received an automated phone call from the Israeli military. It warned people in Arabic to stay away from members of Hamas and other terrorist groups in Gaza and not to cooperate with them "because they are risking your lives." The message told people not to use their homes to store arsenals for terrorist groups. "Anyone who is present in these buildings risks their lives."

On Monday, Israel dropped fliers telling residents that terrorist groups and those who smuggle weapons continue to hide among residents even though they know they are "always a target for the Israel Defense Forces." It warned that those activities create dangers for residents and their children. The fliers provided phone numbers and e-mail addresses for Gazans to secretly provide information about militant activities.

The Israeli military's Operation Protective Edge against Hamas is part of an effort "to restore a state of security," Lerner, the Israeli military spokesman, told CNN on Tuesday.

Teens' deaths sparked new violence

Tensions in the region reached a fever pitch after three Israeli teens, including one dual U.S. citizen, on their way home from school in the West Bank were kidnapped last month. Israel blames Hamas. Their bodies were found last week.

Later in the week, a Palestinian teen was abducted and then found dead within an hour in Jerusalem. Israel has arrested suspects and says there's "strong indication" it was a revenge killing. Amid clashes in the days following, the Palestinian teen's American cousin, who was visiting, was beaten by men in Israeli security uniforms.

Israel also announced a confession in the May killing of another Israeli Jewish teen. The suspect is an Arab resident of northern Israel, and police believe the attack was fueled by Palestinian "nationalism."

Palestinian Authority President Mahmoud Abbas, who was criticized by Palestinians when he condemned the Israeli teens' kidnappings, called on Israel on Tuesday to immediately stop its strikes, warning the operation would drag the region into instability.

Abbas said a truce was needed to "spare the innocent from mass destruction."

And presidential spokesman Nabil Abu Rdainah accused Israel of carrying out an "open massacre" against children, women and the elderly, WAFA reported. He said Israel is making a "decision to expand the war," which he said will drag "the region into a spiral of bloody violence" that "will burn everyone."

Long-range threat

Israel says the aim of its offensive is to strike Hamas in Gaza and stop rocket fire into Israel that threatens civilians. Hamas is estimated to have 10,000 rockets of varying ranges, Lerner said, including some that can reach as far north as Tel Aviv and beyond.

Israel confirmed that a rocket hit the city of Hadera, which is some 62 miles (100 kilometers) from Gaza.

"They have substantial armaments which can strike the soft underbelly of Israel," Lerner said.

He said the Israel Defense Forces' position had changed from focusing on de-escalation to preparing for a deterioration of the situation.

'Red lines' crossed

The conflict between the two sides has worsened in the past few days.

"The enemy has crossed the red lines and will be made to pay the price for its crimes," Mushir Al-Masri, a Hamas leadership figure and member of the Palestinian parliament, wrote on his Facebook page Monday. "The blood of our martyrs is precious ... and is fuel for the intifada and the resistance."