Security officials said dozens of troops were killed, along with nearly 100 attackers.
The restive territory's deadliest fighting in decades followed the assassination of Egypt's chief prosecutor and a vow by President Abdel-Fattah el-Sissi to step up the legal battle against Islamic militants.
Later Wednesday, a special forces team raided a Cairo apartment and killed nine fugitive members of the outlawed Muslim Brotherhood, including a former member of parliament, security officials said.