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.
The new order 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 authorised 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.
PTI