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.
The airstrike caused heavy damage to the building, and set off a scene of panic as crowds of people, some of them bloodied, fled the smoldering remains. Screaming Palestinians took away motionless bodies, including what appeared to be the two children.
Recent weeks had seen a pattern of limited rocket fire and limited airstrikes in retaliation, and Israel signaled it would halt it aerial campaign if quiet was restored.
But as the rocket fire intensified, senior Israeli officials have said the campaign could be prolonged.
Prime Minister Benjamin Netanyahu has instructed the military to prepare options for every scenario, including a potential ground invasion.
"We will not tolerate rocket fire on Israel cities, and we are preparing to expand the operation with everything at our disposal to strike Hamas," said Israeli Defense Minister Moshe Yaalon, who announced a special state of emergency in southern Israel.
Military spokesman Lt. Col. Peter Lerner said Israel would continue its barrage so long as its citizens were under fire from Gaza. "We don't expect it to be a short mission on our behalf," he said.
Palestinian President Mahmoud Abbas called on Israel to halt the airstrikes immediately and appealed for calm.
"The Palestinian leadership is conducting intensive and urgent contacts with regional and international parties to stop the escalation," he said.
Abbas, however, has little influence over a Gaza Strip. Hamas took control of Gaza in 2007, and despite a recent unity deal that ostensibly handed control back to Abbas, the militant group remains the dominant power there. Smaller and more radical forces than Hamas are also involved in rocket fire from Gaza.
Shaul Shay, a military analyst at the Interdisciplinary Center Herzliya, said it was too early to predict how long the operation would last, and Israel would likely evaluate whether to expand it on a daily basis depending on the actions of Hamas.
He said that without recapturing the Gaza Strip and ousting Hamas, it would likely end like other campaigns on recent years - with a de facto truce that would tentatively hold until another round of violence.
"Israel prefers not to go to larger scale conflict and escalation but it depends mainly on the other side," he said. "The only question is how much damage there will be before we return to the same understandings. It is more or less the same game."
The military says Hamas has amassed about 10,000 rockets, including longer-range rockets that can reach central Israel. The military ordered hundreds of thousands of Israelis within a 40-kilometer (25-mile) radius of the Gaza Strip, including Israelis in the major southern city of Beersheba, to stay indoors and near shelters.
The renewed rocket fire from Gaza comes as Hamas is increasingly isolated and under pressure from Egypt, where the new regime ousted its former patron the Muslim Brotherhood.
Israel is also cracking down on the organization's West Bank operation following last month's kidnapping and killing of three Israeli teenagers in the West Bank. Israel blames Hamas for the teens' abduction and is conducting a manhunt for two Hamas-affiliated Palestinians in the West Bank it believes carried out the kidnapping and killing.
Tensions have been high since the three Israeli teenagers were kidnapped June 12 in the West Bank and were later found dead. That was followed by last week's slaying of the Palestinian youth. Six Jewish suspects have been arrested.
The charged climate inspired President Barack Obama to pen an op-ed for the Israeli newspaper Haaretz.
"All parties must protect the innocent and act with reasonableness and restraint, not vengeance and retribution," Obama said in the piece published Tuesday.
Obama warned of a "dangerous moment" for the region after the collapse of U.S.-backed peace talks.
"As I said last year in Jerusalem, peace is necessary, just, and possible. I believed it then. I believe it now," he wrote. "Peace is necessary because it's the only way to ensure a secure and democratic future for the Jewish state of Israel."
Heller reported from Jerusalem.