were carried out overnight, according to Israeli television.
Palestinian medics said 38 Gazans have been killed and 345 wounded since Israel launched the aerial campaign on the Palestinian enclave on Wednesday, with at least four militants among the eight people killed in the latest raids.
Since the start of its operation, Israel's army says militants have fired more than 580 rockets over the border, 367 of which hit southern Israel, and 222 of which were intercepted by the Iron Dome anti-missile system.
In the same period, three Israelis have been killed and 13 injured, including 10 soldiers.
On Saturday, a rocket lightly wounded four Israeli soldiers, as police spokeswoman Luba Samri said rocket fire was down on previous days, with 16 counted in the morning.
The military said it had sealed off all main roads around Gaza and declared a closed military zone, in the latest sign it was poised to launch a first ground offensive on the Palestinian territory since December 2008-January 2009.
"The IDF (army) has targeted Ismail Haniya's headquarters in Gaza," a army spokesman told AFP, referring to the Hamas prime minister.
The army also said it had targeted Hamas government buildings, the interior ministry and the police compound, as well as militant training facilities and 'dozens of terror sites.'
Haniya's Islamist government said four 'barbaric Israeli' strikes 'completely destroyed' its headquarters and that neighbouring houses were damaged.
Correspondents at the scene said the building, deserted for fear of attack, had been flattened and reduced to a pile of rubble but there were no reports of casualties.
Air strikes on Rafah in southern Gaza killed five people and three people died in an Israeli raid on a refugee camp in central Gaza, medics said.
Saturday's violence came as Tunisian Foreign Minister Rafik Abdessalem crossed into Gaza through the Rafah border crossing with Egypt, a day after a solidarity visit by Egypt's premier.
AFP correspondents in Gaza City reported a heavy bombardment in the city's west, after raids on the Hamas police headquarters in the same area and the government's internal security headquarters in the north.
Tanks were seen massing along the Gaza-Israel frontier on Friday, and a steady stream of reservists arrived throughout the day.
President Barack Obama reiterated US support for Israel's right to defend itself during a call with Israeli Prime Minister Benjamin Netanyahu about the conflict.
Israeli ministers approved the call-up of as many as 75,000 reservists as Netanyahu held late evening talks in Tel Aviv with his key ministers, Channel 2 television reported.
Hamas's military wing said it fired a rocket at Jerusalem, and witnesses said another crashed into the sea off Tel Aviv on Friday.
The two rockets were the farthest Gaza militants have ever fired into Israel, exceeding even the 60 kilometres (36 miles) achieved by a rocket that hit the sea off Jaffa, just south of Tel Aviv, on Thursday.
Neither caused any casualties or damage, but they sowed panic in both of the Jewish state's main population centres, setting off warning sirens and sending people scurrying to shelters.
UN and Palestinian officials said UN chief Ban Ki-moon would travel to the region in days to push for a truce.
"Ban went to the region during the last Israeli offensive against Gaza in 2009 and worked hard to end that conflict. He is looking to produce a truce and ceasefire this time as well," one senior UN diplomat said.
But as ground troops massed, there was no let-up in Israeli air attacks.
A child was among the dead reported by the territory's emergency services on Friday, two of whom were brought in to Gaza City's Shifa hospital as Egypt's Prime Minister Hisham Qandil toured the wards on an unprecedented solidarity visit.
Washington appealed to Egyptian leaders as well as to allies such as Turkey to use their sway with the Palestinians in a flurry of telephone diplomacy aimed at containing the crisis.