Hamas, the Islamist group that runs the Gaza Strip, said Israeli planes bombed the office building of Prime Minister Ismail Haniyeh - where he had met on Friday with the Egyptian prime minister - and struck a police headquarters.
Despite the violence, Tunisia's foreign minister arrived in the coastal enclave early Saturday in a show of Arab solidarity, heading to a hospital to visit the wounded.
Officials in Gaza said 38 Palestinians, half of them civilians including eight children and a pregnant woman, had been killed in Gaza since Israel began its air strikes. Three Israeli civilians were killed by a rocket on Thursday.
Rocket fire by militants into Israel resumed after dawn following a relative lull overnight, but the number was still lower than on the previous three days since the start of the offensive, an Israeli military spokesman said.
A three-storey house belonging to Hamas official Abu Hassan Salah was also hit and completely destroyed early Saturday. Rescuers said at least 30 people were pulled from the rubble.
The Israeli army said it had targeted a number of government buildings during the night, including Haniyeh's office, the Hamas Interior Ministry and a police compound.
On Friday, Palestinians fired a rocket toward Jerusalem for the first time in decades. Tel Aviv, Israel's commercial centre, also came under rocket attack for the second straight day, in defiance of Israel's air campaign that began on Wednesday with the declared aim of deterring Hamas from launching cross-border attacks that have plagued southern Israel for years.
Hamas claimed responsibility for firing at Jerusalem and Tel Aviv. Israel said the rocket launched toward Jerusalem landed in the occupied West Bank, and the one fired at Tel Aviv did not hit the city. There were no reports of casualties or damage.
The siren that sounded in Jerusalem stunned many Israelis. The city, holy to Jews, Muslims and Christians, was last hit by a Palestinian rocket in 1970. It was not targeted when Saddam Hussein's Iraq fired missiles at Israel in the 1991 Gulf War.
Prime Minister Benjamin Netanyahu held a four-hour strategy session late on Friday with a clutch of senior ministers in Tel Aviv on widening the military campaign, while other cabinet members were polled by telephone on increasing mobilisation.
Political sources said they decided to more than double the current reserve troop quota set for the Gaza offensive to 75,000. It did not necessarily mean all would be called up.
Egypt's Prime Minister Hisham Kandil paid a high-profile visit to Gaza on Friday, denouncing what he described as Israeli aggression and saying Cairo was prepared to mediate a truce.
Egypt's Islamist government is allied with Hamas but also party to a 1979 peace treaty with Israel.
"Egypt will spare no effort ... to stop the aggression and to achieve a truce," Kandil said.
A Palestinian official with knowledge of Cairo's mediation efforts said on Saturday that Egypt was pursuing a truce.
"Egyptian mediators are continuing their mediation efforts and these will intensify in the coming hours," he told Reuters.
The Israeli military said some 150 rockets fired from Gaza had hit Israel since Friday and at least 83 more were intercepted by its Iron Dome anti-missile system.
In a further sign Netanyahu might be clearing the way for a ground operation, Israel's armed forces decreed a highway leading to the territory and two roads bordering the enclave of 1.7 million Palestinians off-limits to civilian traffic.
Tanks and self-propelled guns were seen near the border area on Friday, and the military said it had already called 16,000 reservists to active duty.
Netanyahu is favoured to win a January national election, but further rocket strikes against Tel Aviv, a free-wheeling city Israelis equate with New York, and Jerusalem, which Israel regards as its capital, could be political poison for the conservative leader.
U.S. President Barack Obama commended Egypt's efforts to help calm the Gaza violence in a call to Egyptian President Mohamed Mursi on Friday, the White House said, and underscored his hope of restoring stability.
In a call with Netanyahu, Obama discussed options for "de-escalating" the situation, the White House added.
Obama "reiterated U.S. support for Israel's right to defend itself, and expressed regret over the loss of Israeli and Palestinian civilian lives," a statement on the call said.
Israel Radio's military affairs correspondent said the army's Homefront Command had told municipal officials to make civil defence preparations for the possibility that fighting could drag on for seven weeks. An Israeli military spokeswoman declined to comment on the report.
The Gaza conflagration has stoked the flames of a Middle East already ablaze with two years of Arab revolution and a civil war in Syria that threatens to leap across borders.
It is the biggest test yet for Mursi, a veteran Islamist politician from the Muslim Brotherhood who was elected this year after protests ousted military autocrat Hosni Mubarak in 2011.
Egypt's Muslim Brotherhood are spiritual mentors of Hamas, yet Mursi has also pledged to respect Cairo's 1979 peace treaty with Israel, seen in the West as the cornerstone of regional security. Egypt and Israel both receive billions of dollars in U.S. military aid to underwrite their treaty.
Hamas fighters are no match for the Israeli military. The last Gaza war, involving a three-week long Israeli air blitz and ground invasion over the New Year period of 2008-2009, killed more than 1,400 Palestinians, mostly civilians. Thirteen Israelis died.
U.N. Secretary-General Ban Ki-moon is expected to visit Israel and Egypt next week to push for an end to the fighting in Gaza, U.N. diplomats said on Friday.
Hamas refuses to recognise Israel's right to exist. By contrast, Palestinian President Mahmoud Abbas, who rules in the nearby West Bank, does recognise Israel, but peace talks between the two sides have been frozen since 2010.
Abbas' supporters say they will push ahead with a plan to have Palestine declared an "observer state" rather than a mere "entity" at the United Nations later this month.