The military arm of the Palestinian terrorist organisation Hamas, the Qassam Brigades, attacked the Israeli border, crossing Kerem Shalom with rockets on Tuesday.
According to the Israel Defence Forces (IDF) the Qassam Brigades claimed responsibility for the attacks which triggered warning sirens in the area.
It said there was no initial information on casualties.
The Qassam Brigades had on Sunday attacked Kerem Shalom with around 10 rockets, killing four Israeli soldiers and injuring others.
Kerem Shalom, the most important border crossing for the delivery of aid from Israel to the Gaza Strip, was then closed.
An Israeli military officer had said on Tuesday before the new attack that the crossing was still closed.
However, efforts were being made to reopen it as soon as possible.
International aid organisations have repeatedly warned of hunger among the civilian population in Gaza Strip.
In response, Israel has allowed more aid supplies into the coastal strip in recent weeks.
