One of the men has been in immigration detention in Arizona for 18 months, while the other was recently released on bail while his asylum claim is heard in court.
Mounis Hammouda and Hisham Shaban fled Gaza several years ago and spent months traveling from Cyprus through Central America to get to the US.
They are part of a global refugee crisis emanating from the Middle East that has touched off a political uproar in Europe and the US.