Five Palestinians were killed by Israeli air strikes on Thursday morning, as militants shot around 250 rockets into Israel, killing three Israelis.
The latest violence raised the total number of Gazans killed in 20 hours of Israeli air strikes to 13. At least 120 other residents of the coastal enclave have been injured, according to medics.
In the same period, Gaza rockets killed three Israelis and injured another five in a direct hit on a residential building in the southern town of Kiryat Malahi, said Israeli police.
"We have three killed," spokeswoman Luba Samri told the AFP news agency, saying four other people were also injured in a "direct hit on a house" in the town, 30km north of the Gaza Strip.
The fighting began when Israel assassinated Ahmed al-Jabari, head of Hamas’ military wing, with an air strike on his car in Gaza on Wednesday. Jabari's bodyguard and son were also killed in the strike.
Thursday's rocket fire on Kiryat Malahi was claimed by Jabari's group, the Ezzedine al-Qassam Brigades, in a statement on its website.
Israeli authorities said more than 250 rockets and mortars were fired by Hamas and other armed groups from Gaza as of Thursday afternoon, and its Iron Dome interceptor missile system had shot down dozens of the projectiles.
On either side of the frontier, people fled streets for cover.
Expecting days or more of fighting, Israel warned Hamas all its men were in its sights and weathered censure from
influential Arab countries - with the Arab League announcing it was to hold an emergency meeting on Saturday and Egypt recalling its ambassador to Israel.
The United States condemned Hamas, long shunned by the West as an obstacle to peace.
Speaking on Wedneday night, hours after a major wave of air strikes pounded targets in the Palestinian Gaza Strip, Netanyahu vowed that Israel would not tolerate any further rocket fire on its territory.
In a televised address, Netanyahu said: "Today we sent a clear message to Hamas and other terrorist organisations, and if it becomes necessary we are prepared to expand the operation.
"Hamas and the terror organisations have chosen to escalate their attacks on the citizens of Israel in recent days," he said after consultations with his security cabinet.
"We will not tolerate a situation in which Israeli citizens are threatened by rocket fire."
Al Jazeera's Nadim Baba, reporting from Gaza, said: "In the last 30 seconds there was another big blast. [The strikes] have been going on all evening.
"It is not just air strikes, but also strikes from Israeli naval ships just off the coast of Gaza."
Baba said the streets of Gaza City on Wednesday evening were "eerily quiet, except for the sound of ambulances".
"The latest from medical sources is that at least seven people have been killed, including two children, and at least 60 people have been wounded, including ten children."
'Gates of hell'
The Ezzedine al-Qassam Brigades, the armed wing of Hamas headed by Jabari, issued a communique saying Israel had "opened the gates of hell on itself", and Hamas spokesman Fawzi Barhum said the strike was tantamount to a "declaration of war".
"The occupation committed a dangerous crime and crossed all the red lines, which is considered a declaration of war", he said in a statement.
"The occupation will pay dearly for this and we will make it regret the moment they thought about it."
Hamas said it had fired at least 20 rockets into Israel in retaliation for Jabari's assassination, shortly after the air strike tore his car to pieces.
Mark Regev, spokesperson for the Israeli prime minister's office, told Al Jazeera: "We are continuing to hit Hamas targets, and their missile sites, because we knew they would [be] responding immediately...Ultimately we did not want this round of fighting, it was forced upon us.
"We will not allow Hamas to terrorise our civilian population. All the options are open.
"Our most important goal is to protect our people. Hamas has deliberately targeted civilians. They deliberately use Gaza civilians as human shields, too."
The strikes came after five days of rising tensions along the Gaza border which began on Saturday when Palestinian fighters fired an anti-tank rocket at an army jeep, sparking Israeli fire which killed seven.
Ehud Barak, the Israeli defence minister, said the strike was only the beginning of an operation with the goals of strengthening Israel's deterrence, damaging armed groups' rocket-firing capabilities and stamping out attacks on southern Israel.
"Israel doesn't want a war but the Hamas provocation of recent weeks, with recurring, frequent rounds of mortar and rockets fired at southern Israel, an explosive tunnel that was activated...and anti-tank fire at a jeep in Israel, forced us to act sharply and decisively," Barak said.
"We are at the beginning, not end of this action," he said, stressing the need to be "on high alert in Israel and West Bank... It won't be a quick fix.. but we'll reach goals we set for this operation."
He urged regional leaders to act "judiciously and with a cool head to promote stability and return of quiet, and not to be dragged to their deterioration".
The operation prompted widespread condemnation, with Egyptian President Mohamed Morsi recalling Cairo's envoy to Israel and summoning the Israeli ambassador for consultations, his spokesman said.
Following a request from Morsi, Arab League chief Nabil el-Arabi said the organisation was preparing to hold an emergency meeting over the violence.
Britain also urged restraint and Russia said it was "very concerned" about the escalation, while Washington said it was watching developments in Gaza "closely".
Israeli army spokeswoman Avital Leibovich said the operation, code named "Pillar of Defence", had only just begun with the air force hitting "close to 20 targets" used for launching rockets, especially those with a range of 40km, and causing "significant damage".