The three-page order would undo many of the restrictions on handling detainees put in place under president Barack Obama to roll back practices authorized during George W. Bush's administration, The New York Times reported.
It would revoke the directive that gives the Red Cross access to all war detainees in US custody, and would order the Pentagon to continue to use the Guantanamo military prison facility in Cuba "for the detention and trial of newly captured" detainees, including Islamic State jihadists, according to the Times.
A Trump spokesman denied that the document had originated in the White House.
"I have no idea where it came from, but it is not a White House document," White House press secretary Sean Spicer told reporters.
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The Times published a copy of the draft executive order, entitled "Detention and Interrogation of Enemy Combatants," on its website.
It says US spy agencies, in consultation with the attorney general, shall review current intelligence needs and "recommend to the president whether to reinitiate a program of interrogation of high-value alien terrorists to be operated outside the United States, and whether such program should include the use of detention facilities operated by the Central Intelligence Agency."
In December, after meeting with retired general James Mattis, Trump said he was "impressed" with Mattis's argument that building trust and rewarding cooperation by detainees worked better than waterboarding.
Mattis has since been sworn in as secretary of defense.
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