A Hamas leader on Tuesday threatened to not move forward into the next phase of the Gaza ceasefire agreement until more pressure is placed on Israel to open up a key border crossing, cease deadly strikes and allow more aid into the Palestinian territory.

With the remains of one hostage still in Gaza, the first phase of the U.S.-brokered ceasefire in the war between Israel and Hamas is nearly complete, after a two-month process plagued by delays and fi...