Four officials say the administration's decision follows pressure from the Pentagon and State Department. They had urged the White House to reconsider Iraq's inclusion given its key role in fighting the Islamic State group.
Trump is expected to sign the new order Wednesday. It is designed to replace an earlier Trump order that was blocked by federal courts.
The officials spoke on condition of anonymity because they weren't authorized to discuss the order before it is signed.
They said six countries — Iran, Libya, Somalia, Sudan, Syria and Yemen -— will remain on the travel ban list.
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