The revised draft was circulated inside the National Security Council on Thursday, with a deadline for concurring or providing comment by Friday, one official said. The official said the draft had been held much more closely than the original one had been, apparently to prevent further leaks.

The White House had distributed its original draft executive order on detainees in an email to council staff members at 8:41 a.m. on Jan. 24, giving them until 10 that morning to provide any comment. It was one of at least five significant draft orders distributed to them at the same time and with the same quick deadline, two of which Mr. Trump signed in the next few days.

The staff members urged the White House to slow down and get input from affected agencies and departments. They forwarded the email with the draft executive order on detainees to other officials in the government, who provided it to still other people, until it was leaked. The text of the original draft was first reported by The New York Times on Jan. 25.

In response to the news reports, the White House press secretary, Sean Spicer, falsely said that the draft was not a “White House document.” After The Times then reported details about when and how the White House had circulated it, Mr. Spicer said that it had not been “derived from White House sources” and suggested that its origins traced to input provided to the Trump transition effort.

As BuzzFeed reported, the Trump draft order had lifted verbatim sections from a draft order written in 2012 by policy advisers to the Mitt Romney campaign. But the language in the Trump White House version had been revised, including to take account of subsequent legal and geopolitical developments and to substitute terms like “fight against radical Islamism” for “global war on terrorism.”

By Jan. 27, Mr. Trump foreshadowed that his flirtation with reviving a C.I.A. interrogation program had come to an end, at least for the time being.

At a news conference, Mr. Trump said that while he personally supported waterboarding and thought torture worked, Mr. Mattis, who opposes torture, “will override because I’m giving him that power.”