The children, aged eight, nine, 11 and 12, were killed as they played in a field during an Israeli air strike around the northern town of Jabaliya, Palestinian medics said.
Another 12-year-old boy died of wounds sustained in a Gaza raid the previous day, and a shepherd was killed in northern Gaza.
The Israeli army said it carried out several air strikes targeting rocket-launching sites.
Palestinian medical sources said three people were killed in two separate air strikes in the northern Gaza Strip on Thursday evening, two of them in one car. The third was found dead in an electricity company vehicle, they said.
Thirty-two Palestinians and one Israeli have now been killed in two days of bloodshed, all but three of them in and around the impoverished Gaza Strip, where Israel has imposed a punishing blockade.
Among those killed have been a six-month-old baby in Gaza and a man in southern Israel who became the first Israeli victim of a Gaza rocket attack in nine months.
A Hamas gunman was also killed in an Israeli strike near the house of Ismail Haniya, the premier in the Hamas-led government that Palestinian president Mahmud Abbas fired after the Islamists seized control of Gaza in June.
Following talks with US Secretary of State Condoleezza Rice in Tokyo, Olmert vowed to punish Hamas for the rocket attacks despite US concerns about civilians in Gaza.
"We will make the terrorists pay a very heavy price," Olmert told reporters. "We are at the height of this battle and we will pursue it until the danger threatening residents in the south ends."
Defence Minister Ehud Barak warned that "a large-scale ground operation is being considered" and Foreign Minister Tzipi Livni urged the international community to accept such an operation.
Rice said earlier she told Olmert that she supported his determination to end the Palestinian rocket attacks. "The issue is that the rocket attacks need to stop."
She is due to visit the Middle East next week as part of Washington's efforts to advance the peace process that was relaunched in late November but has made little progress since.
The UN Relief and Works Agency for Palestinian refugees called on Israel "to abide by international law and exercise maximum restraint, and not to endanger civilians".
"The killing of innocent children is always tragic and condemnable," UNRWA spokesman Chris Gunness told AFP.
The escalation in Gaza and nearby Israeli towns is causing "unacceptable distress and danger from the ongoing risk of attack", said the International Committee of the Red Cross.
Haniya blasted the "successive crimes committed by the Zionist occupation" and called on Arab countries to "stop their regrettable silence and act with urgency to stop the aggression."
The Palestinian government based in the West Bank also denounced "abominable Israeli crimes" in Gaza.
The latest outburst of violence around Gaza flared early on Wednesday when an Israeli strike killed five Hamas militants in the southern town of Khan Yunis.
In retaliation, the Islamists launched a volley of rockets into southern Israel, killing a man at a university on the outskirts of the town of Sderot, the first Israeli killed by rocket fire from Gaza since May.
At least 232 people, most of them Gaza militants, have been killed since the revival of Israeli-Palestinian peace talks three months ago, according to an AFP tally.
The bloodshed comes as Israel's US ally steps up its diplomacy in the Middle East in the hope of sealing a peace deal between Abbas and Olmert before President George W. Bush leaves office in January.
On Thursday, Israeli troops also killed two militants in the northern West Bank town of Nablus, medics and security sources said.
On the Israeli side, two people were lightly wounded after Gaza militants fired more than 20 rockets and mortar rounds into the Jewish state, the army said.
In his talks in Japan, Olmert cast doubt on whether the goal of striking a deal by the end of 2008 was realistic.