Mortar rounds struck a residential area south of the town of Sheikh Zuweid in North Sinai late on Monday in which the two boys were killed, medics said.
Earlier a roadside bomb struck an armoured military vehicle on the Egyptian side of the divided city of Rafah on the Gaza border, killing an army officer and two soldiers.
Another soldier was also wounded when the bomb hit the vehicle in the Tawil al-Amir district.
Jihadists who have pledged allegiance to the Islamic State group, which controls swathes of Iraq and Syria, said they carried out the bomb attack.
"We blew up an armoured vehicle of the apostate army and everyone inside was killed," IS Sinai Province said on a Twitter account attributed to the group.
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In a separate incident, four IS fighters were killed when they attempted to attack a checkpoint in North Sinai's provincial capital of El-Arish, police said.
The army meanwhile said on its Facebook page that 57 "terrorists" were killed over the past 10 days in clashes with security forces in the peninsula.
Formerly known as Ansar Beit al-Maqdis, the IS group has carried out repeated deadly attacks on the security forces in its peninsula stronghold.
Twin bomb attacks claimed by the group on April 12 killed at least 14 people, 11 of them security personnel.
On April 2, the group launched simultaneous attacks on five checkpoints in the region that killed 15 soldiers and two civilians.
The group says its attacks are in retaliation for a deadly crackdown by the security forces on Islamists since then army chief and now President Abdel Fattah al-Sisi ousted his Islamist predecessor Mohamed Morsi in 2013.
The attacks have come despite stringent security measures imposed by the army in the province, including a night-time curfew and the creation of a buffer zone along the Gaza border to prevent militants infiltrating from the Palestinian territory.