Israeli air strikes launched before dawn on Tuesday killed two Palestinians and destroyed much of one of Gaza's tallest apartment and office buildings, setting off huge explosions and wounding 20 people, Palestinian health officials said.
Israel had no immediate comment on the attacks that took place as Egyptian mediators stepped up efforts to achieve an elusive ceasefire to end seven weeks of fighting.
Palestinian health officials say 2,125 people, most of them civilians, including more than 490 children, have been killed in Gaza since July 8, when Israel launched an offensive with the declared aim of ending rocket fire into its territory.
Sixty-four Israeli soldiers and four civilians in Israel have been killed.
Palestinian officials said 70 families lived in the 13-storey building, which was listing to one side after the blasts. The structure also housed offices and a shopping complex.
Hundreds of neighbors in surrounding homes were also evacuating to avoid being hurt if the structure collapses, witnesses said.
Fatalities were averted by warnings to residents to vacate the premises and two non-explosive warning missiles fired by drones.
The attacks followed a day of heavy rocket fire at Israel, whose military said more than 130 rockets and mortar bombs were fired from Gaza on Monday, one of them injuring a civilian.
Militants resumed rocket fire at Israel after daybreak and a rocket struck a house in the southern coastal town of Ashekelon, lightly wounding 10 people, police said. Another was intercepted over the Tel Aviv area, an army spokeswoman said.
Hamas claimed responsibility for firing rockets at Tel Aviv, at least one of which was shot down by Israel's Iron Dome interceptor. Warning sirens were also heard in Israeli communities bordering Ben-Gurion International Airport.
Israeli air strikes on Tuesday killed at least nine Palestinians in Gaza.
Two rockets were fired at Israel across the Lebanese border as well after nightfall on Monday. The Israeli military said it responded by firing artillery shells at the "source of the attack". There were no reported injuries on either side.
Despite the raging violence, there were signs the sides might be edging towards a new ceasefire.
Egypt proposes indefinite truce
Qais Abu Leila, a senior Palestinian official involved in Egyptian-mediated talks to reach a truce, said Cairo had proposed an indefinite ceasefire.
Israeli media said a deal could come within hours. Several earlier truces have collapsed after a few days.
Cairo's latest initiative calls for the immediate opening of Gaza's crossings with Israel and Egypt to aid reconstruction efforts in the coastal strip, to be followed by talks on a longer-term easing of the blockade.
Hamas and Israel blamed each other for delaying agreement, and the negotiations have been additionally complicated by the fact both sides refuse to talk to each other and communicate only indirectly, largely via Egyptian intermediaries.
An Israeli official speaking on condition of anonymity said Israel would consider the proposal once assured that Hamas was ready to accept it.
Hamas has said it will not stop fighting until the Israeli-Egyptian blockade on the enclave of 1.8 million people is lifted.
Both Israel and Egypt view Hamas as a security threat and are demanding guarantees that weapons will not enter the economically crippled territory. Israel recalled its negotiators from Cairo last Tuesday after the last ceasefire collapsed.
The United States has separately begun preparing its own draft outline for a proposed United Nations resolution to demand a ceasefire, working alongside European powers and Jordan on a final draft, diplomats said on Monday.
Thousands of homes in the Gaza Strip have been destroyed or damaged in the conflict. Nearly 500,000 people have been displaced in the territory where Palestinians, citing Israeli attacks that have hit schools and mosques, say no place is safe.
Israel has said Hamas bears responsibility for civilian casualties, because it operates among non-combatants. The group, it said, uses schools and mosques to store weapons and as launch sites for cross-border rocket attacks.
Israel took steps on Tuesday to protect its economy from further war damage.
The Bank of Israel, fearing the conflict will slow economic growth, cut its benchmark interest rate by a quarter-point to 0.25 percent, its lowest level. The bank said the war might shave half a point off GDP, which is forecast at 2.9 percent in 2014, as tourism and consumer spending are hit.