JERUSALEM — Three Israeli teenagers were missing in the West Bank and were presumed to have been kidnapped, Israeli military officials said on Friday. The episode tested Israel’s already strained ties with the Palestinians and prompted the involvement of the State Department amid reports that one of the youngsters held United States citizenship.

Secretary of State John Kerry called President Mahmoud Abbas of the Palestinian Authority and Prime Minister Benjamin Netanyahu of Israel. A State Department official said, “We are working the issue as hard as we can.”

Mr. Netanyahu said he held Mr. Abbas responsible for the well-being of the missing teenage boys, who were studying at a religious high school and seminary in the West Bank.

The crisis comes at a delicate time, after the collapse this spring of American-brokered peace talks and less than two weeks after the establishment of the new Palestinian government that resulted from a reconciliation pact between the Palestine Liberation Organization, which is dominated by Mr. Abbas’s mainstream Fatah movement, and Hamas, the Islamic militant group that dominates Gaza.