The operation has been given the code name "Operation Protective Edge."
IAF fighter planes and aircraft are currently flying sorties over Gaza targeting terror targets, Israel Radio reported.
Heavy rocket barrages slammed into southern Israel on Monday evening, triggering air raid sirens across wide areas, including the Hof Ashkelon Regional Council, Sderot, Rehovot and Beit Shemesh.
Seven long-range Palestinians rockets were intercepted over Ashdod, and five over Netivot.
Some 30 rockets were fired from Gaza in the Monday night barrage. A total of 80 rockets slammed into southern Israel throughout the day and evening.
The attacks came shortly after a senior military source said the IDF is taking “significant steps” to prepare itself for a stepped up campaign of attacks against Hamas in Gaza. He spoke as Palestinian projectile fire from the Strip continued unabated.
(Video: Iron Dome interceptions, filmed from Rehovot)
The Iron Dome defense system intercepted seven rockets over Ashdod on Monday night and five over Netivot after Gaza terrorists fired a barrage of projectiles at southern Israel. A man in Ashdod was injured from shrapnel.
Sixteen projectiles also landed in open areas near the southern city of Beersheba, according to the IDF Spokesperson's Unit.
Air raid sirens were heard on Monday in the outskirts of Jerusalem and Tel Aviv, but an Israeli police spokesman said they were false alarms.
The armed wing of Hamas Izz al-Din al-Qassam took responsible for the latest barrage of rocket fire on Israel on Monday night.
The Home Front Command has instructed the municipalities of Ashkelon, Ashdod, Beersheba, and Gaza border communities to open public bomb shelters in anticipation of long-range Hamas rocket attacks.
"We can't avoid dealing with Gaza because there is noise [security developments] in other arenas," the source said, referring to rioting by Arab Israelis and in Palestinian districts of east and north Jerusalem.
The IDF's steps to enhance preparedness on the Gaza border include the calling up of 1,500 reserves, and the setting up of infantry assault units on the Gaza border, in case "a decision is made" for an offensive in Gaza, the source said.
"We are ready for an escalation," the source said, adding that Hamas is not only failing to prevent other terror groups from firing projectiles at southern Israel, it is taking an active and dominant part in the recent attacks.
Most of the projectiles landing in southern Israel are mortar shells, and the rate of rocket fire is low, the source said, but all of the projectile fire has to stop, he added.
"We're taking steps now... ahead of the possibility that the escalation increases. We're preparing for a gradual increase in the use of force, and increasing our rate of attacks [on terror targets in Gaza]," he stated.
A majority of the reserves will be sent to unit headquarters and Home Front Command units, and some are Border Police who will replace conscripted forces currently on duty in the West Bank, freeing them up for deployment to Gaza.
"The message to Hamas is clear. A ceasefire without conditions," the source said. "Last Thursday, I said quiet would be met with quiet. Now, we see that this hasn't happened."
Addressing the deaths of seven Hamas members in a tunnel in south Gaza, the source said they died as a result of explosives they planted in an underground assault tunnel aimed at an IDF target. "This was designed to enable a significant terror attack," the source said. "In recent days, we have operated in this area, and we will continue to act against the threat of tunnels in the coming days," he added.
The seven Hamas members did not die as a result of an Israeli air strike, the source explained. The tunnel was found by the army a few days ago. "Last night, for reasons that are unclear, Hamas decided to handle the explosives. They handled bombs that were in the tunnel, and were ready to go off against military targets. The explosives went off, leading to seven casualties," said the source.
The Security Cabinet met Monday for the fourth time in eight days, amid the continuous pounding of the western Negev from the Gaza Strip, the tension in Jerusalem, and rioting in some Israeli-Arab areas.
Earlier, on Sunday night, the IDF struck a terrorist rocket launching crew in Gaza that was "about to launch a rocket" at Israel, he added. The cell did not belong to Hamas. Two of its members were killed in the air strike.
The Israel Air Force struck an attack tunnel in southern Gaza that was aimed at carrying out a terror attack against Israeli civilians, the IDF said Monday evening. The air strike is a "targeted defensive measures" carried out in accordance with the latest security evaluation, the IDF added.
The Israel Air Force struck 18 targets across Gaza between Sunday night and Monday afternoon, and Palestinian sources said nine combatants - seven of them Hamas members - were killed in the Strip.
Two members of a Palestinian rocket launching crew were killed in central Gaza in an IAF strike. The IDF said the men were preparing to fire rockets into southern Israel.
A few hours later, the IAF launched two waves of air strikes, striking nine targets in the first wave, and five targets in the second. Most of the targets were underground rocket launchers and terrorist operations centers.
Seven Hamas fighters were killed and four people were wounded in the attacks, Hamas's armed wing, the Al-Kassam Brigades, said in a statement.
Hamas spokesman Sami Abu Zuhri accused Israel of committing a "grave escalation" and threatened to retaliate, saying Israel would "pay the price."
Throughout Monday, terrorists in Gaza fired rockets at southern regions near the Gazan border, and fired one long-range projectile at Be'ersheba in the morning as well. The latter rocket exploded in an open area outside of the city, triggering air raid sirens. There were no injuries or damages in that attack.
The IAF struck three underground rocket launchers in northern Gaza in the late afternoon.
Rocket fire persisted in the Sha'ar Hanegev, Sdot Negev, Eshkol, and Sderot regions. A soldier was lightly injured by shrapnel from a rocket on Monday in Eshkol. By midday, some 15 projectiles fired from Gaza exploded in southern regions, and that number grew to 20 by 2 pm.
An IDF unit carrying out routine operations on the border with southern Gaza came under fire on Monday morning. The unit was attacked with an RPG and gunfire. Soldiers returned fire into Gaza. There were no injuries among soldiers in the cross-border attack.
Khaled Abu Toameh, Herb Keinon and Reuters contributed to this report.