Saying it was responding to the rocket attacks, Israel has tightened its closure of Gaza borders, choking off some food supplies to the territory and raising international concern.
The violence has strained a ceasefire in place since June, which is due to run out later this month.
Sherine Tadros, Al Jazeera's correspondent in Gaza, who was speaking outside the Abu Yousuf hospital in Rafah, said: "Sources here are telling us that the two people who died were in fact two boys aged between 15 and 18.
"And the head nurse has told us that these two boys were in fact civilians playing in an area near the old Gaza airport. They have also confirmed that four other people were injured, two of them critically.
"We should say that no Palestinian group has so far claimed that their fighters have been killed. We should also stress that the Israeli army insist that the target of the air strike was in fact Palestinian fighters that were firing mortars towards Israeli soldiers."
Meanwhile, in the West Bank, Jewish settlers desecrated mosques in two villages by spraying graffiti insulting the Prophet Mohammed.
Insults written in Hebrew were spray-painted on the walls of a mosque in Al Sawyeh village in the northern West Bank, Mohammed Abdelrahim, a local councillor, said.
The perpetrators also sprayed stars of David on the doors of several stores and slashed the tyres of eight cars in a pre-dawn attack, Abdelrahim said.
Settlers also painted stars of David and the word "Hebron" on two mosques in the villages of Sinjel et Turmusayya.
Hebron was the scene of clashes on Monday between security forces, Palestinians and settlers who have defied a court order to leave a house whose ownership is disputed.
Five Palestinians, including a 12-year-old boy, were injured in the violence, Palestinian doctors said.
|The settlers say they bought the house from a Palestinian who denies the deal [AFP]
Settlers and Palestinians threw stones at each other and at least two cars belonging to Palestinians were set ablaze in what the Israeli army described as a "riot".
Thirteen settler families, who have been facing eviction for 18 months - have vowed to resist an Israeli court order to leave the building in Hebron that they insist they bought from Palestinians.
The settler families have occupied the building, which they call the "house of peace", since March 2007.
An unnamed eyewitness told news agency AFP that Palestinians were hurt by stone-throwing settlers who also "shot at the Palestinians but did not wound anyone".
An Israeli army spokesman said: "Two settlers were wounded, and the army, border guards and police were trying to separate the two sides."
Israeli officials said an Israeli teenager had suffered a serious head injury after Palestinians dropped a large rock on him during violence in the city.
Clashes frequently occur between both sides because of a settler enclave established in the heart of Hebron and a further 6,500-strong settlement living in Kiryat Arba on the outskirts of the city.
Meanwhile, European politicians told Tzipi Livni, Israel's foreign minister, on Tuesday that her country had to do more to stop the expansion of West Bank settlements.
The European parliament's foreign affairs committee said settlers' moves were threatening Israeli-Palestinian peace efforts.
Livni, in Brussels to seek closer ties with European Union, said it was no longer official Israeli policy to expand settlements in the West Bank and the government had been trying to reduce them since peace talks restarted last year.
Speaking to the committee, she said: "We are not trying to use or abuse the period of time in which we negotiate in order to have more land, or to get more land from the Palestinians."
The foreign minister said "minor" efforts by some settler groups around the West Bank town of Hebron to expand their settlements would not derail peace talks or efforts to set up a Palestinian state.
She sat through a barrage of criticism levied by several members of the committee, and also faced questions about what Israel was doing to alleviate the situation in Gaza.
Livni said Israel was allowing in humanitarian aid to ease the crisis there.