One person was lightly injured when a rocket fired from the Gaza Strip struck an Ashkelon cemetery.
Another rocket exploded inside the city. Hamas, which controls Gaza, took responsibility for Monday’s strikes.
The victim suffered shrapnel wounds to his neck. Several people suffered from shock and were treated at the scene.
Later in the day, Israeli forces killed a Palestinian in an attack on a rocket squad in Gaza.
Earlier Monday, Israeli troops shot and killed three Palestinian terrorists on Gaza’s boundary fence. The Islamic Jihad members were spotted trying to plant a mine against Israeli border patrols east of the Gazan town of Khan Younis.
An Israeli airstrike nearby wounded three other Hamas gunmen.
There were no Israeli casualties in the earlier incidents, which came as Egypt tries to broker a truce between the Jewish state and Islamist Hamas.