An aggressive Iran has resulted in broader common ground between Israel and many of the Sunni Arab governments in the region.
The plan ended speculation as to whether his administration would abandon a "two-state resolution" to the conflict.
Despite carrying out deadly attacks throughout the world over the past years, ISIS has rarely targeted Israel.
Israel destroyed a series of what it said were attack tunnels, dug under the border by the Lebanese militant group Hezbollah.
The lifting of the travel ban partially reverses an order issued last month, restricting travel to all of Israel's West Bank.
Chairman of the Joint Chiefs of Staff Gen. Mark Milley met Sunday with Israeli counterpart Lt. Gen. Aviv Kohavi.
Travel to the West Bank, including Jericho, Bethlehem and Jerusalem's Old City, is restricted "until further notice."
Israel reiterated that it was willing to abide by the cease-fire if there are no additional rocket attacks.
Secretary of State Pompeo also outlined his vision for a forthcoming plan for peace between Israelis and Palestinians.
Speaking alongside Israeli PM Netanyahu, Bolton said no one has granted Iran a "hunting license in the Middle East."