Trump is expected to sign the executive order in the coming days.
Four officials told The Associated Press that the decision followed pressure from the Pentagon and State Department, which had urged the White House to reconsider Iraq's inclusion given its key role in fighting the Islamic State group.
Citizens of six other predominantly Muslim countries Iran, Libya, Somalia, Sudan, Syria and Yemen will remain on the travel ban list, said the officials, who spoke on condition of anonymity because they weren't authorised to discuss the order before it is signed. Those bans are effective for 90 days.
The officials also said the order won't include any explicit exemption for religious minorities in the countries targeted by the travel ban. Critics had accused the administration of adding such language to help Christians get into the US while excluding Muslims.
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The White House did not respond to a request for comment. Trump signed his original executive order in late January. It sparked immediate confusion, panic and outrage as some travelers were detained in US airports before being sent back overseas and others were barred from boarding flights at foreign airports.
The State Department provisionally revoked roughly 60,000 valid visas in all, before a federal judge in Washington state blocked the government from carrying out the ban. The 9th US Circuit Court of Appeals upheld that decision.
Under the revised order, officials said, all existing visas will be honored.
In his first address to a joint session of Congress, Trump on Tuesday evening defended his effort.
"We will shortly take new steps to keep our nation safe and to keep out those who would do us harm," he said.