ALEXANDRIA, Va. — Federal prosecutors concluded their conspiracy and terrorism case against a British member of the Islamic State on Wednesday with a wrenching account of how an aid worker had been brutalized and sexually assaulted during a year and a half in captivity.

For much of her ordeal, the aid worker, Kayla Mueller, 24, was held by a notorious cell of four Islamic State members known for their viciousness and nicknamed “the Beatles” for their British accents, muffled behind black balaclavas.

Prosecutors say the defendant, El Shafee Elsheikh, 33, is “Ringo.” For nearly two weeks, they have argued that the polite, bespectacled defendant was a central figure in the Beatles, responsible for drafting ransom emails and mistreating prisoners. Among those captives, they say, were Ms. Mueller and three American men — James Foley, Steven J. Sotloff, and Peter Kassig — who were later beheaded by one of Mr. Elsheikh’s close associates.

In his closing remarks, the assistant U.S. attorney, Raj Parekh, asked jurors to pay particular attention to the suffering endured by Ms. Mueller, who was not only physically abused like the other American captives, but treated as a slave in the months leading up to her death, under mysterious circumstances, in early 2015.

“And what about Kayla?” Mr. Parekh asked, as her parents sat stone-faced in the gallery of the ninth-floor courtroom outside Washington. “She was held as a slave. She was locked in a room, threatened, raped, never allowed to communicate with her family.”

Prosecutors have charged Mr. Elsheikh, who was born in Sudan and raised in London, with four counts of conspiracy related to the abduction of Westerners, the murder of prisoners and his support of terrorist groups. He faces four additional counts of hostage-taking that resulted in the deaths of Ms. Mueller, Mr. Foley, Mr. Sotloff and Mr. Kassig.

Mr. Elsheikh has not been directly implicated in the killing of the Americans, but his participation in, and knowledge about, numerous kidnapping, ransom and murder plots is enough to secure a conviction under the law, prosecutors have argued.

The British extremists repeatedly beat the hostages they kept imprisoned in Raqqa, Syria, which the Islamic State claimed as its capital at the time, according to prosecutors. They subjected their hostages to abuses including waterboarding, mock executions, painful stress positions, food deprivation, chokeholds that caused blackouts, electric shocks and beatings that lasted 20 minutes or longer. They also forced their hostages to fight each other and to witness killings, court papers said.

Over the past two weeks, the government has introduced testimony from freed hostages who detailed the sadism of the cell members. But the hostages were often blindfolded, and their captors were careful to always wear masks — making definitive physical identification difficult.

The prosecution team is, therefore, leaning heavily on Mr. Elsheikh’s own public comments about his actions. He gave at least seven news interviews after being captured by Kurdish forces and turned over to the U.S. military in 2018, disclosing knowledge of key operational details and his own role in seeking to extract millions in ransom payments for Western hostages.

Near the end of his summation, Mr. Parekh replayed one interview for the jury, who leaned in to hear the scratchy audio on a flat-screen TV.

Mr. Elsheikh was asked if he opposed slavery, in light of Ms. Mueller’s experience.

“No, I don’t denounce slavery,” he said.

Prosecutors are cherry-picking evidence to compensate for the lack of a witness who could clearly identify him as a member of the cell, a defense lawyer, Nina J. Ginsberg, said in her closing argument.

She tried to convince the jury that Mr. Elsheikh’s interviews in 2018 were motivated less by guilt than by fear he would be handed back to the Kurds for a quick trial and summary execution in Iraq, and that he was making a desperate effort to encourage American prosecutors to indict him.

“He became, at that time, committed to repeating these admissions in the hopes of being sent to the U.S. for a fair trial,” Ms. Ginsberg said.

Mr. Elsheikh’s appearance in an American courtroom, once seen as a long shot, is the product of intense political and legal wrangling. In August 2020, the attorney general at the time, William P. Barr, agreed to waive the death penalty against Mr. Elsheikh and Alexanda Kotey, a member of the cell, in exchange for cooperation from British prosecutors — seen as a key element in obtaining a conviction.

Last September, Mr. Kotey, 38, pleaded guilty to multiple charges, including conspiracy to commit hostage-taking resulting in death and conspiracy to murder American citizens outside the United States. As part of the plea deal, if Mr. Kotey fulfills his cooperation requirements, he could be sent to Britain after 15 years to complete the remainder of a mandatory life sentence.

The families of the American victims, who had gathered briefly for Mr. Kotey’s sentencing last fall, have been present for Mr. Elsheikh’s court proceedings, with some testifying about their interactions with the hostage takers.

This week, they gathered in small groups, or slumped against courtroom walls during breaks, visibly drained by hours of testimony that have included images and descriptions of their loved ones’ deaths. The families had pressured Mr. Barr to move quickly on the case, but the effort came with a cost.

“Why didn’t he just take a deal too?” Carl Mueller, Kayla’s father, asked of Mr. Elsheikh.

“For two weeks, we’ve had to sit here and live through all the gruesome details,” he added, his voice strained. “It’s extremely emotional.”