Mr. Graham is a longtime advocate of holding terrorism detainees in military custody. He was upset after the Trump administration used the civilian criminal justice system to handle two new terrorism suspects — an apparent Islamic State sympathizer who ran over people with a truck in New York, and a man suspected of participating in the 2012 attack on the consulate in Benghazi, Libya, who was captured in that country.

Government lawyers had maintained that there was no clear legal authority to place either man in military custody because there was insufficient evidence that either was part of a group covered by Congress’s Authorization for Use of Military Force, or A.U.M.F., against the perpetrators of the Sept. 11, 2001, attacks.

But Mr. Graham argued for a less restrictive interpretation that would permit such newly captured suspects to be held in military custody for a period of interrogation without defense lawyers. He met separately in December with Mr. Sessions, Mr. Mattis and Mr. Kelly to argue that the administration was keeping the Obama-era approach, which he saw as misguided, and was promised that the Trump team would start a policy review.

Mr. Graham is also said to have proposed one alternative procedure: using Guantánamo to hold new terrorism suspects when they are captured abroad, and using the military brig in Charleston, S.C., for future terrorism suspects arrested on domestic soil. It remains unclear what policy Mr. Mattis will recommend.

One problem with using Guantánamo is the legal risk that would be created by sending an Islamic State suspect there, as opposed to the Qaeda and Taliban suspects sent there years ago. It is contested whether the A.U.M.F. can be legitimately interpreted to cover the war against the Islamic State, as the government contends. Guantánamo detainees have the right to file habeas corpus lawsuits challenging their detention in court, so sending an Islamic State suspect there would give a judge an opportunity to rule against the government — jeopardizing the legal basis for the broader war effort.

In theory, Congress could solve that problem by specifically authorizing the use of military force against the Islamic State, also known as ISIS. On Tuesday, Mr. Trump appeared to throw his support behind that idea, saying, “I am also asking the Congress to ensure that, in the fight against ISIS and Al Qaeda, we continue to have all necessary power to detain terrorists — wherever we chase them down.” (It was then that Mr. Trump ad-libbed his line that many would now go to Guantánamo.)

But Congress has been debating since 2014 whether and how to enact an Islamic State-specific A.U.M.F. It has been paralyzed by a lack of consensus over whether to impose new limits on the war effort, like limiting its duration, geographic scope and extension to associated forces.