Harf, the State Department spokeswoman, said the FAA makes its "decision based solely on the security and safety of American citizens, period."
Catherine Frazier, a spokeswoman for Cruz, said the Obama administration's foreign policy was itself "ridiculous and offensive."
In a statement, the powerful American Israel Public Affairs Committee, which holds considerable sway with Congress, expressed concerns with the FAA ban and urged a review of the policy.
AIPAC said Israel has been subjected to hundreds of rockets the past two weeks and air travel has been safe and uninterrupted.
"The American people have shown in this difficult moment that they stand strongly with our democratic ally," AIPAC said. "Now is not the time to send the entirely wrong message with a ban on flights to Israel."