Jerusalem (CNN) -- A spike in violence between the Israeli military and Palestinian militants in Gaza, along with a cross-border attack into Israel from Egypt, has left six Palestinians and one Israeli dead over the past two days, officials said Tuesday.
Also, a Palestinian child was killed when a rocket launch attempt by Palestinian militants backfired, Israel said.
An al Qaeda-affiliated group was involved in the cross-border attack, an Egyptian official said.
Palestinian medical officials said Israeli airstrikes had killed six Palestinians in Gaza: Four Palestinians were killed in Beit Hanoun, a city in northern Gaza, and two more early Tuesday east of central Gaza City, the medical officials said. The Palestinian Cabinet, which meets in the West Bank, issued a statement saying six Palestinians were killed in Gaza.
The Cabinet also cited as "martyrs" two Palestinians who were killed by an Israeli settler in Hebron, in the West Bank.
The Israeli military said a group of Palestinians on Sunday "attempted to pull an Israeli civilian out of his car (while) threatening and beating him. The civilian opened fire at the attackers. He was injured and evacuated to a hospital to receive treatment." A hospital spokesman said two men who were shot were pronounced dead at a hospital Sunday.
Meanwhile, Israel carried out air raids against targets in Gaza as militants fired numerous rockets into southern Israel.
By evening, 25 rockets were fired into southern Israel on Tuesday, the Israel Defense Forces said.
The armed wing of Hamas said it had shelled an Israeli military base. Israel did not say immediately whether a base was hit.
The Izzedine al Qassam Brigades said some rockets it fired into Israel hit "the Zionist settlement of Re'im."
The Israel Defense Forces said its aircraft targeted "a terrorist squad" in Gaza that was responsible for the rockets. "A hit was confirmed," the IDF said in a statement.
On its official Twitter feed, the IDF reported that Palestinian militants caused the death of a Palestinian child when a rocket launch backfired. Between 10% and 15% of rocket launch attempts from Gaza backfire, the IDF said.
"During 2012, over 290 rockets were fired at Israel from the Gaza Strip. The IDF will not tolerate any attempt by terrorist groups to target Israeli civilians and IDF soldiers, and will continue to operate against those who use terror against the state of Israel," the statement said, adding that Hamas "is solely responsible for any terrorist activity emanating from" Gaza.
But the Palestinian Cabinet slammed "the continuous Israeli escalation against our people."
Monday's attack, on the Israeli side of the border with Egypt, was the work of Palestinian Islamic Jihad and al Qaeda, according to a North Sinai intelligence officer who spoke on condition of anonymity because he was not authorized to speak to the media.
In a statement, a group calling itself the Religious Council of Mujahedeen said it was behind the attack "in the name of the great martyr Osama bin Laden." It identified the two attackers as an Egyptian and a Saudi.
The Israeli military said it killed two infiltrators in the attack.
"Fire was opened at Israeli workers during routine construction work on the security fence between Israel and Egypt. IDF soldiers responded with fire towards the terrorists," the IDF said in a statement.
The Egyptian intelligence officer, a general, told CNN: "We now have to face the reality that al Qaeda is present in Sinai. ... Palestinian Islamic Jihadi factions now present in Sinai, along with al Qaeda cells, are active, and we are tracking them down."
CNN's Michael Schwartz, Kareem Khadder, Talal Abu Rahman, and Josh Levs and journalist Mohamed Fadel Fahmy contributed to this report.