Urging from State Department and Pentagon officials led to the de-listing of Iraq, the AP reported, allegedly because of the work the country has done in fighting the Islamic State in Iraq and Syria.
Earlier in the evening The Wall Street Journal reported, citing people familiar with the planning, that Trump's new order would likely exempt current visa holders in hopes of making the policy more able to withstand legal challenges. One source told the Journal the new order may remove Iraq from the list.
It would also reportedly strike a provision in the previous action that gave preference to refugees who are religious minorities, apparently an appeal to criticism that the ban is targeted specifically at Muslims.
Trump's first order halted the entire refugee program for four months while placing an indefinite stop to the acceptance of Syrian refugees.
Updated at 12:01 a.m.