The United States has more expansive laws for incarcerating people who joined terrorism groups, including the offense of providing material support to a terrorist organization. It also operates the Guantánamo prison, where it holds several dozen terrorism suspects without charges and is trying to prosecute a handful through the troubled military commissions system.

Like many European allies, Britain strongly opposes the Guantánamo prison. Mrs. May’s government was afraid that the Trump administration might send the two British men there, a recurring theme in the ruling.

Last March, the ruling said, the British home secretary at the time, Amber Rudd, met with Mr. Sessions to discuss the case: “In the course of those discussions, he expressed the view that all foreign terrorist fighters should be prosecuted in their home countries. He referred to them as ‘prisoners of war,’ and to Guantánamo Bay as the appropriate place of detention for prisoners of war.”

After discussions with Justice Department officials in April, the British security minister, Ben Wallace, internally argued against pushing for assurances against the death penalty, saying that he had been warned that “there were strong voices arguing for Guantánamo” and that “the more restrictions the U.K. attached to support, the harder it would be to avoid that outcome.”

And on May 30, when the new British home secretary, Sajid Javid, met with Mr. Sessions, the attorney general said that “if the U.S. were to be willing to try Elsheikh in a civilian court as opposed to a military one, he could not see how the U.S. could do that without the U.K. evidence or without recourse to the death penalty.”

Ultimately, Mr. Javid told Mr. Sessions in June that the United States could have the evidence without death-penalty conditions, so long as it was not introduced in the military commissions system. That concession by the British appears to have persuaded senior Trump administration officials to focus on an eventual civilian trial in the Eastern District of Virginia on charges that would most likely include conspiracy in kidnapping resulting in death, an offense that carries the death penalty, according to officials familiar with internal deliberations.

Both Mr. Sessions, who was fired in November, and John R. Bolton, who became President Trump’s national security adviser in April, have agreed that a civilian trial is now seen as the most likely venue, according to former American officials. The family members of the victims had strongly pushed for that outcome. In a meeting with Mr. Bolton in late April, he was visibly emotional and pulled out a handkerchief in response to the families’ arguments, according to several people familiar with the meeting.