The evidence the British gathered was crucial to any trial, former American law enforcement officials said. The men are said to have covered their faces while interacting with the hostages. To strengthen the case beyond a reasonable doubt that they are indeed two of the four Beatles, prosecutors need supplementary material gathered by Britain about their backgrounds, associations, radicalization, movements and activities.

British officials had given in to American demands that its prosecutors receive the evidence without strings attached in part because the British feared that the alternative was that the Trump administration would send the two Britons to the American military prison at Guantánamo Bay, Cuba.

Families of victims of the Beatles have opposed that idea both as a matter of symbolism — ISIS dressed Western hostages in Guantánamo-style orange jumpsuits before murdering them, including James Foley, the American journalist who was beheaded in August 2014 — and as a matter of substance. The military commissions system at the base has proved to be dysfunctional and incapable of getting contested cases swiftly to trial.

In a brief interview, Mr. Foley’s mother, Diane Foley, urged the Trump administration to prosecute the men in federal court even without the death penalty. “Not prosecuting them is immoral,” she said. “They need to be held accountable for their horrible crimes.”

Ms. Foley said she opposed the death penalty for the detainees, adding that it would only “fulfill their desire for martyrdom.”

The British government has also balked at sharing evidence if the men are sent to Guantánamo, raising the prospect of indefinite detention without a trial. Moreover, transferring them there would set up a court battle that executive branch officials want to avoid: whether the government’s claim is valid that Congress’s 2001 authorization to fight Al Qaeda also covers the use of armed force against the Islamic State in Syria.

British officials initially sought assurances from the United States that it would not seek the death penalty in exchange for providing the evidence, as is routinely the case. But the Trump administration refused to grant them. American law enforcement officials wanted to seek capital punishment and argued that since the British government essentially was not handling its own mess, it should not place restrictions on the United States.