GAZA: 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 neighbours 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.