Four rockets hit open fields in the Eshkol region and the mortar shell landed in the Sdot Negev area, resulting in no casualties or property damage being reported, The Jerusalem Post said.
The attack prompted Israeli Defense Minister Ehud Barak to order the closure of border crossings between Gaza and Israel, which affects scheduled deliveries of humanitarian aid, the newspaper said.
Officials said Israeli soldiers Monday killed an Islamic Jihad militant during a West Bank operation.
The militant Jihad organization said it may not renew its shaky cease-fire agreement with Israel, which expires Friday, if Israel targeted its members in the West Bank.
"Our rockets will not stop and it will be like the rain over all the Zionist towns around the Gaza Strip," said Abu Hamza, an Islamic Jihad spokesman.
Members of Hamas, which controls the Gaza Strip, was scheduled to meet Islamic Jihad, the Popular Resistance Committees and other groups to discuss next steps regarding renewing the cease-fire agreement.