The new order will replace the old order that was blocked by the federal courts.
Trump is expected to sign the executive order in the coming days.
Late on Tuesday night, multiple outlets reported that the White House chose to hold off on issuing the new executive order after seeing the positive reviews for Trump's impersonation of a competent president.
President Donald Trump's revised travel ban order will exclude Iraq, but continue to impose restrictions on the other six Muslim-majority nations that were included in the original order, United States officials said.
"I don't think the travel ban is going to help in any significant way", Brennan said on CBS News' "Face the Nation."
Brennan added that it would be more important to focus on terror recruitment online rather than taking a person's country of origin into account when deciding how to bar potential terrorists from the U.S.
Sources told The Associated Press the decision followed pressure from the Pentagon and State Department, which urged the White House to reconsider Iraq's inclusion on the list, given Iraq's key role in fighting ISIS.
No other reasons were offered for the delay, but one factor may be a Department of Homeland Security report that contradicted the White House, saying citizenship in one of the seven Muslim-majority countries included in the ban is "unlikely to be a reliable indicator of potential terrorist activity".
The administration could potentially argue that the existing challenges to the original executive order are moot, but the challengers tell CNN the legal battles will likely continue even after the new order is signed. It's expected to only apply to future visa applicants from the seven (or six) countries, not legal permanent residents or current visa holders.
The Trump administration wants the new order to better stand up to legal scrutiny than the first measure, which Trump signed in late January.
The new order also removes an exception to the refugee prohibition for religion minorities, the person said.
White House officials said green-card holders were exempt after the first order was issued, but the group had been originally banned along with visa holders. "That discriminatory taint can not be removed simply by eliminating a few words or clever tinkering by lawyers".