Hamas claimed responsibility for the mortar fire, and shortly after the attacks Palestinian sources reported that three Hamas operatives were killed and a number of others were wounded in an Israel Air Force strike in the Gaza City neighborhood of Sajaiya.
The sources reported the men were part of a special unit of Hamas' military wing, the Izz al-Din al-Qassam Brigades.
The mortars, which were fired in two separate salvos, landed in open areas near Nahal Oz, causing no injuries or damage.
Residents were asked to remain indoors amid warnings of additional attacks.
Alon Shuster, head of the Sha’ar HaNegev Regional Council expressed concern over the increasing rocket fire: "This is the time to make immediate decisions. This kind of fire on civilians is unacceptable. The government cannot afford to take its time on this.
"Unfortunately, Israeli has no definitive answer to the rocket fire," he added. "We don't know when the Iron Dome (rocket-intercepting) system will become operational, or even if it will be able to protect us. The government has to make some sort of a decision – political or military – but it has to make it now."
Earlier Tuesday, at around 11:15 am, two Qassam rockets fired from the northern Strip landed in open areas in the Negev. Two more rockets fired toward the southern region at 7:30 am landed within Sdot Negev Regional Council limits and south of Ashkelon. No injuries or damage were reported in either attack.
On Sunday, the eve of Shavuot, a foreign worker from Thailand sustained shrapnel injuries when a Qassam fired from Gaza hit a western Negev community.
Ali Waked contributed to the report