President Trump recently issued an executive order to keep the Guantánamo prison open, although his administration so far has taken no new detainees there. Senator Lindsey Graham, a South Carolina Republican who is a proponent of using wartime detention for terrorism cases, has been pushing the administration to take Mr. Kotey and Mr. Elsheikh to Guantánamo.

But Defense Secretary Jim Mattis, whom Mr. Trump has tasked with leading a policy review about what to do with newly captured terrorism suspects, does not want the military to take on the headache of holding the men in long-term detention and prosecuting them in the troubled military commissions system, the officials said.

Mr. Mattis’s reluctance, coupled with the British demands, means bringing Mr. Kotey and Mr. Elsheikh to American soil for civilian court prosecution is seen as far more likely. The Justice Department is now trying to decide whether the Southern District of New York or the Eastern District of Virginia would handle the prosecution, the officials said.

Some prosecutors and F.B.I. agents in New York have argued that they should get the case because their area of operations includes Western Europe, and the suspects are Londoners. But their counterparts in Virginia and the F.B.I.’s Washington Field Office have already been handling most of the casework related to the killings of American hostages in Syria, according to an official familiar with the deliberations.

In February 2016, for example, federal prosecutors in Virginia charged the wife of an Islamic State leader in the death of Kayla Mueller, an American, although the United States military transferred her to the Iraqi justice system.

Ms. Mueller was kidnapped in August 2013 and is believed to have been sexually abused by a leader of the Islamic State, which later said she died in an airstrike in early 2015. The British-accented captors tortured prisoners under their control, according to former hostages; Mr. Kotey is suspected of being a particularly brutal one whom the prisoners called George.

The parents of four Americans who were kidnapped by the Islamic State and abused in various ways before their killing — Ms. Mueller and three men who were beheaded, James Foley, Steven Sotloff and Peter Kassig — recently wrote an Op-Ed in The New York Times calling on the United States government to prosecute the suspects in civilian court and not to seek the death penalty.