Several hours earlier, a Qassam rocket exploded in an open area near the town of Sderot. There were no reports of injuries or damage.
Sha'ar Hanegev Regional Council head Alon Schuster said that the area's residents were forced to deal with this situation for many years.
"It appears that the negotiations (for a truce) are not only being held in Cairo and in other places, but through shells and rocket fire as well. We, the council heads, cannot advise the army of government how to act. We are busy dealing with ways to allow the residents to live their normative life as best as possible in the framework of this rocket fire, and the government must understand and implement this.
"If the residents continue to suffer these firing and continue to live here, it means they can deal with it, but the government must provide them with the solutions to do so."
On Sunday morning, a Qassam rocket exploded in an open area near the border fence in the Sha'ar Hanegev Regional Council. On Saturday night, a rocket hit southern Ashkelon at around 10:20 pm after an air raid siren sounded in the city's southern industrial zone. There were no reports of injuries or damage in all incidents.
Also Monday, an Israel Air Force assault helicopter fired at a suspicious vehicle near the Kissufim crossing, on the Gaza Strip border. At the same time, a Golani force entered the Strip and exchanged fire with Palestinian gunmen attempting to plant explosive devices along the border. The ground force directed the chopper to the suspicious vehicle.
Palestinian sources reported that the gunmen opened fire at an Israel Defense Forces patrol near the border fence, and that the soldiers fired back. There were no reports of injuries in the strike, which took place east of the al-Maazi refugee camp.
The same area has seen several clashes with gunmen planting explosive devices recently.
The Southern Command has been working on various channels in recent weeks in order to thwart attacks initiated by Hamas and other Palestinian organizations, including attempts to kidnap soldiers.
Ilana Curiel contributed to this report