Hamas fires rockets into Israeli border town in response to killing of its soldiers.
Six people were also wounded in the attack.
Shortly afterwards, two Islamic Jihad fighters were killed and two wounded in an air raid in the central Gaza Strip, medics said.
“The military carried out an air raid in the central Gaza Strip against a vehicle loaded with weapons and carrying terrorists that was headed to carry out an attack,” an Israeli spokesman said.
A third Israeli raid, which witnesses said was carried out by either helicopters or drones, killed an Islamic Jihad fighter and wounded two more south of Gaza City, medical sources said.
Islamic Jihad named the dead man as Mohammed Abdullah, 40, a senior commander of its Al-Quds Brigades military wing.
Last week, Israeli forces killed Majed al-Harazin, Islamic Jihad’s Gaza commander, and 12 other fighters in a series of raids.
Thursday’s deaths brought to 6,005 the number of people killed since the start of the second Palestinian uprising in September 2000, the vast majority of them Palestinians, according to an AFP tally.
In the West Bank, the Israeli army announced it had arrested Mohammed Abdel Rahman, a wanted member of the Islamic Jihad.