Jerusalem (CNN) -- Israel intercepted a rocket fired at Tel Aviv on Tuesday and killed militants who stormed into Israeli territory, the military said, as people on both sides of the Gaza border were living under a barrage of attacks from the air.
In a dramatic escalation of the conflict, militants fired more than 130 rockets at Israeli civilians, Israel said. Palestinians reported 24 people in Gaza were killed and more than 150 injured in Israeli airstrikes. Israel said it targeted about 150 "terror sites" in Gaza.
The warning sirens that blared in Tel Aviv, one of Israel's most populated areas, showed a threat Israel had warned of. The country said militants' rockets from Gaza are powerful enough to reach 3.5 million Israeli citizens. "Hamas will pay a heavy price for its vicious attacks on millions of Israeli civilians," the Israel Defense Forces said on Twitter.
"No nation would accept constant rocket fire. Neither will we," the IDF said, using the hashtag #ItMustStop.
Islamic Jihad, another Palestinian militant group, took responsibility for the rocket fired at Tel Aviv. In a statement, the group called it a "response to the ongoing Zionist aggression."
Hamas controls Gaza. Israel has said it holds Hamas responsible for the actions of militant groups inside the territory.
Hamas, on Twitter, used the hashtag #Gazaunderattack and warned, "Retaliations are coming, it is a matter of time."
Hamas later claimed responsibility for firing rockets on Jerusalem and Haifa. Three explosions sounded just west of the capital. There were no immediate reports of casualties.
"The occupation started this aggression and it must pay the price. We will be the ones to define the cost of the bill," Hamas spokesman Fawzi Barhoum posted on his Facebook page.
The possibility of an Israeli incursion into Gaza loomed, with the Cabinet authorizing the military to call up 40,000 troops if needed -- 10,000 more than were called up during Israel's offensive into Gaza in November of 2012. Lt. Col. Peter Lerner, a military spokesman, said that only about 1,000 have been called up so far. He referred to "possible ground maneuvers."
Israeli Intelligence Minister Yuval Steinitz told CNN a ground operation "might become necessary."
But it was Hamas that claimed responsibility for "storming" into Israeli territory Tuesday. Hamas-controlled television reported "from the heart of the battlefield" that a group of its "commandos" was "conducting its duties in Zikim Zionist military base according to plan."
Zikim lies just north of Gaza and south of the Israeli city of Ashkelon. The group of militants tried to enter Zikim through the water, Israeli media reported. Israeli soldiers spotted the divers in the water and called in an infantry force, Israel's Channel 10 reported. An exchange of fire ensued.
Israel responded by infantry, air force, and navy, Lerner said. Five attackers -- armed with Kalashnikoves and hand grenades -- were killed, the Israel Defense Forces said. One Israeli soldier was lightly wounded, and the situation was ongoing as of Tuesday evening on the beach near the military's base in Zikim, he said.
Meanwhile, Hamas said it blew up a tunnel under Karem Shalom, an Israeli town near Gaza's southern border. The town's residents were ordered to turn off all lights in their homes, Channel 10 reported. Israeli aircraft hovered above and fired toward Gaza, the station said.
People in 'human shield' killed on Gaza rooftop
Among the dead in Gaza was Mohammad Sha'aban, a leader of Hamas' militant wing, Palestinian sources said. Israel confirmed that Sha'aban, "a senior Hamas terrorist," was killed. Another militant was killed in an Israeli airstrike on an open field in Gaza.
Several Palestinians were killed in an airstrike on a Gaza rooftop. Palestinian medical sources told CNN the death toll was 10, but then lowered it to seven. Official Palestinian news agency WAFA reported that six were killed. Those killed were forming a "human shield" on the roof of a home belonging to members of Hamas' militant wing, Palestinian sources said. Two were children, WAFA and Palestinian medical sources said.
The home was near another home belonging to the same Hamas members that Israel struck Monday night, Palestinian sources said.
Palestinians said another of the 24 killed was a child who died of wounds after an airstrike on a motorcycle.
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."
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."
After that statement, the barrage of rockets from Gaza into Israel increased, with Hamas claiming responsibility.
The conflict is creating strains within the governing coalition of Israeli Prime Minister Benjamin Netanyahu.
Foreign Minister Avigdor Lieberman, head of the Yisrael Beiteinu party, said in a news conference Monday that he told Netanyahu of his intention to dissolve his party's joint faction with Netanyahu's Likud party, saying it was "not working."
Lieberman criticized Netanyahu's handling of Gaza.
Tensions are also increasing between Hamas, which controls Gaza, and the more moderate Palestinian Authority in the West Bank.
CNN's Diana Magnay reported from Jerusalem; and Ed Payne and Josh Levs reported from Atlanta. CNN's Kareem Khadder, Ben Wedeman, Jethro Mullen, and Jason Hanna contributed to this report.