An Israeli army spokesman said on Tuesday: "Palestinians launched two Qassams at Israel a short time ago and they both landed north of the Gaza Strip. One landed in an open area and one landed in an area of the Ashkelon industrial zone."
The rocket fell in a "sensitive location" a military source said, but added that there were no casualties or damage.
The armed wing of the Islamic Jihad faction claimed to have fired a rocket on Ashkelon.
After the latest attack, Israeli artillery continued to bombard the northern Gaza Strip, where a block of flats was earlier damaged, security sources and witnesses said.
One Israeli shell caused widespread damage to two apartments in the northern town of Bait Hanun although there were no immediate reports of casualties, the sources said.
Earlier rocket attacks were claimed by the Al-Aqsa Martyrs' Brigades, a faction affiliated to Fatah.
Al-Aqsa later claimed to have fired two additional rockets at the Israeli village of Kfar Aza, but a security source said remains of only four rockets were found in total on Tuesday, although further projectiles had been launched.