Monday's violence comes amid rumors of a possible ceasefire that neither side would confirm.
Senior Hamas official Izzat al-Rishq said no agreement has yet been reached while another Hamas official, Osama Hamdan, acknowledged that "efforts are underway to stop the Israeli aggression."
In response to a request for comment about a possible ceasefire, TIME reported that a senior Israeli official suggested "exercising caution" about such reports.
The Egyptian Foreign Ministry urged both sides to agree to a ceasefire on Sunday that has no time limits and to rejoin peace negotiations.
Meanwhile, Palestinian President Mahmoud Abbas announced on Saturday that he has "diplomatic and political solutions" to solve the larger Israel-Palestine conflict and that he plans to introduce his own Mideast peace proposal, sparking speculation that it could be modeled after the 2002 Arab Peace Initiative, also known as the Saudi Peace Initiative.
According to the Palestinian Health Ministry, at least 2,122 people, mostly civilians, have been killed since Israel launched Operation Protective Edge on July 8. Israeli officials reported 64 soldiers and four civilians, one of whom was a Thai national, have been killed.