The secretary of state said the United States and Iran were passing messages to each other as he headed to France for a diplomatic meeting of the Group of 7 nations.
Energy Secretary Chris Wright said the Strait of Hormuz, a critical passageway for oil shipments, remained unsafe for tankers. Iran has been firing projectiles and laying mines.
The ordered departure of U.S. employees in the kingdom indicates that senior diplomats are bracing for a possible surge in violence in the war with Iran, officials say.