Israeli warplanes bombed targets in and around Gaza city, where tall buildings trembled. Plumes of smoke and dust furled into a sky laced with the vapour trails of outgoing rockets.
Egyptian President Mohamed Mursi said in a televised address to the nation that Israel's attacks on the Gaza Strip were "unacceptable" and would lead to instability in the region.
In a telephone conversation with U.S. President Barack Obama, Mursi said he had discussed "ways to reach calm and end the aggression".
The Palestinian Islamist group Hamas claimed it had fired a one-tonne, Iranian-made Fajr 5 rocket at Tel Aviv in what would be a major escalation, but there was no reported impact in the Israeli metropolis 50 kilometres (30 miles) north of the enclave.
Israel's sworn enemy Iran, which supports and arms Hamas, condemned the offensive begun by the Israel Defence Forces (IDF) as "organised terrorism".
Israel was more concerned about the mood in Egypt, whose new Islamist government brokered a truce between the two sides on Tuesday only to see it shattered a day later when Israel assassinated the top Hamas military commander.
Hamas is an offshoot of the Muslim Brotherhood which now controls Egypt, Israel's most powerful Arab neighbour and a crucial partner in the 1979 peace treaty that stands between fragile stability and regional chaos.
Cairo had condemned the offensive and recalled its ambassador from Israel.
Israel's ambassador left Cairo on what was called a routine home visit and Israel said its embassy would stay open.
The dominant Muslim Brotherhood, spiritual mentor of Hamas, called for a 'Day of Rage' in Arab capitals on Friday.
In Lebanon, the Iranian-backed Shi'ite militia Hezbollah denounced Israel's strikes on Gaza as "criminal aggression" and called on Arab states to "stop the genocide".
Hezbollah has thousands of fighters and some 50,000 rockets in southern Lebanon aimed at the Jewish state, according to the Israeli army. But the northern front remained quiet.
The Israeli army said 156 targets were hit in Gaza, 126 of them rocket launchers. It said 200 rockets had struck Israel since the start of the operation, 135 of them since midnight.
Israel's Iron Dome interceptor system, which singles out rockets heading for populated areas, shot down 18 rockets in the first hours of day two of Operation Pillar of Defence, it said.
One of those that got through caught its victims before they could reach the blast shelters that are everywhere in the Negev region, target for sporadic Palestinian rocket attacks from Gaza for the past five years.
Israeli police said the three died when a rocket hit a four-storey building in the town of Kiryat Malachi, some 25 km (15 miles) north of Gaza. They were the first Israeli fatalities of the latest conflict to hit the coastal region.
The offensive began on Wednesday when a precision Israeli air strike assassinated Hamas military mastermind Ahmed Al-Jaabari, and Israel shelled the enclave from land, air and sea.
The 13 killed in Gaza included Jaabari and six Hamas fighters plus six civilians, among them a pregnant woman with twins, an 11-month old boy and two infants, according to the enclave's health ministry. Medics reported at least 130 wounded.
At Jaabari's funeral on Thursday, supporters fired guns in the air celebrating news of the Israeli deaths, to chants for Jaabari of "You have won." His corpse was borne through the streets wrapped in a bloodied white sheet.
But senior Hamas figures were not in evidence, wary of Israel's warning that they are now considered targets.
Expecting days or more of fighting, Israel warned Hamas that all its men were targets. Israeli warplanes dropped leaflets in Gaza telling residents to keep their distance from militants and Hamas facilities.
"The leaflets stress that Hamas is dragging the region toward violence, and that the IDF is prepared to defend the residents of the State of Israel until quiet is restored to the region," the military said in a statement.
The United States condemned Hamas, shunned by the West as an obstacle to peace for its refusal to renounce violence and recognise Israel.
"There is no justification for the violence that Hamas and other terrorist organisations are employing against the people of Israel," said Mark Toner, deputy State Department spokesman.
The U.N. Security Council held an emergency meeting late on Wednesday to discuss the Israeli assault. It called for a halt to the violence, but took no action.
In France, Foreign Minister Laurent Fabious said: "It would be a catastrophe if there is an escalation in the region. Israel has the right to security but it won't achieve it through violence. The Palestinians also have the right to a state."
Oil prices rose by more than $1 as the crisis grew.
Hamas has said the killing of its top commander would "open the gates of hell" for Israel. It also appealed to neighbouring Egypt to halt the "barbaric" assault.
A second Gaza war has loomed on the horizon for months as waves of Palestinian rocket attacks and Israeli strikes grew increasingly intense and frequent.
Israeli Prime Minister Benjamin Netanyahu, favoured in opinion polls to win a January 22 general election, said on Wednesday the Gaza operation could be stepped up.
His cabinet has granted authorisation for the mobilisation of military reserves if required to press the offensive, dubbed "Pillar of Defence" in English and "Pillar of Cloud" in Hebrew after the Israelites' divine sign of deliverance in Exodus.
Israel's Operation Cast Lead in 2008-2009 began with a week of air attacks and shelling, followed by a land invasion of the blockaded coastal strip, sealed off at sea by the Israeli navy. Some 1,400 Palestinians were killed and 13 Israelis died.
Since the rise of Sunni Islamist power in the Arab Spring, Hamas has been emboldened, viewing Mursi as a "safety net" who will not permit a second Israeli thrashing of Gaza, home to 1.7 million Palestinians.
Israel says it has already destroyed much of Gaza's longer-range rocket stockpiles, an assertion seemingly confirmed when Hamas claims of hits on ambitious targets such as Tel Aviv, Ashdod and Israeli naval craft proved unfounded.
Gaza has an estimated 35,000 Palestinian fighters, no match for Israel's F-16 fighter-bombers, Apache helicopter gunships, Merkava tanks and other modern weapons systems in the hands of a conscript force of 175,000, with 450,000 in reserve.