The Israeli military and militants in Gaza are continuing to trade fire, with the round of violence that has followed Israel's killing of Hamas's military chief showing no sign of abating.
Israel hit 200 sites overnight, including PM Ismail Haniya's office.
Gaza militants continue to fire rockets into Israel - one headed for the city of Tel Aviv was intercepted.
Meanwhile, Hamas leader Khaled Meshaal will hold talks with the leaders of Egypt, Qatar and Turkey on Saturday.
At least 40 Palestinians and three Israelis have now died since Israel killed the Hamas military chief Ahmed Jabari on Wednesday.
Israel's military says it still has hundreds of targets it wants to hit in the Gaza Strip.
A spokeswoman also told the BBC that troops gathered near the border were ready to invade should the Israeli government give the order.
The Israeli military spokeswoman told the BBC it did not see any distinction between the military and political wings of Hamas and that anything connected with the militant group was considered a legitimate target.
An Israeli air force spokesman said it had destroyed at least 90% of long-range rockets in Gaza and severely damaged medium- and short-range rockets, and the infrastructure to fire them. However, hundreds of short-range missiles remained, he said.
The BBC's Richard Galpin in Jerusalem says that despite the ferocity of the Israeli bombardment, some 60 rockets were reported to have been fired into Israel on Saturday, with some buildings damaged and four soldiers suffering minor injuries.
Sirens went off around Tel Aviv on Saturday, with Israel's military saying that a missile had been intercepted by a newly installed battery of its Iron Dome defence system.
One rocket also hit an apartment building in the Israeli port city of Ashdod, wounding several.
Israel has now put 75,000 reservists on stand-by, on top of the 16,000 called up in recent days.
Our correspondent says that, so far, there has been no decision on sending in the troops. However, one government minister has been quoted as saying that soldiers could launch a ground offensive into Gaza within the next 24 hours if the rocket fire does not stop.
On Saturday, Gaza City was hit by a string of large explosions shortly after 03:00 (01:00 GMT).
There was another series of strikes in and around the city after 05:00, with several targeting Hamas's cabinet buildings, which correspondents say were likely to have been empty.
Another of the targets was the house of a Hamas leader in Jabaliya, north of Gaza City.
Israel said it was targeting rocket launchers, weapons storage facilities and smuggling tunnels on the border with Egypt in southern Gaza.
Israeli military spokeswoman Avital Leibovich said 200 targets had been hit overnight.
Government spokesman Mark Regev told the BBC the operation would end when Israeli citizens were safe, and that all options - including a ground incursion - remained "on the table".
Militants and civilians, including at least seven children, have been among the Palestinians killed during Israeli strikes in recent days, Hamas says.
Before the recent offensive - codenamed Pillar of Defence - Israel had repeatedly carried out air strikes on Gaza, as Palestinian militants fired rockets across the border.
Hundreds of rockets have been fired into Israel from Gaza since Wednesday.
Most of them landed in the south, but a small number have been aimed at Tel Aviv and Jerusalem.
The three Israelis who died were in a building in the southern town of Kiryat Malachi which was hit by a rocket on Thursday.
A quarter of the attacks have been intercepted by the Iron Dome system, officials say.
Hamas has confirmed Mr Meshaal will meet the Emir of Qatar, Egypt's President Mohammed Mursi and Turkey's President Recep Tayyip Erdogan in Cairo on Saturday night to discuss how a ceasefire can be achieved.
A senior Hamas source in Gaza told the BBC a proposal for a truce made ??by Turkey was being studied by the Hamas delegation in the Egyptian capital.
Ahead of the meeting, Mr Erdogan said: "It's a tactic of Israel's to point the finger at Hamas and attack Gaza.
"Israel continues to make an international racket with its three dead. In fact it is Israel that violated the ceasefire."
Palestinian Authority President Mahmoud Abbas has accused Israel of carrying out "massacres".
Tunisian Foreign Minister Rafik Abdessalem arrived in Gaza through the Rafah border crossing from Egypt to show support for Hamas. Later on Saturday he visited the wreckage of Mr Haniya's HQ.