BOSTON — Federal prosecutors are pressing a judge to let relatives of the 19 people gangster James “Whitey” Bulger was charged with killing make victim impact statements when he is sentenced next month.

Bulger, the former leader of the Winter Hill Gang, was convicted in August of participating in 11 of 19 killings charged in his racketeering indictment. The jury found that prosecutors had not proven he participated in seven of the killings and made no finding in one slaying.

Bulger’s lawyers have argued that only relatives of the 11 victims should be allowed to make impact statements at his sentencing hearing.

But prosecutors argued Friday that Bulger was convicted of two racketeering charges that required the jury to find that he was part of a criminal enterprise responsible for the murders of all the victims, regardless of whether he was the actual killer.

“Thus … family victims of the murder victims clearly have a right to be heard at Bulger’s sentencing,” prosecutors wrote in court documents filed in U.S. District Court.

Bulger’s lawyers argue that allowing relatives of the victims who Bulger was not convicted of killing to give impact statements “trivializes the jury’s function.”

“This court should not consider evidence of these crimes at sentencing,” Bulger’s attorneys, J.W. Carney Jr. and Hank Brennan, wrote in court documents filed last week. “The court should only entertain impact statements and other evidence relating to crimes of which he has been convicted.”

Prosecutors also cited a recent ruling from a federal appeals court in the prosecution of Bulger’s longtime girlfriend, Catherine Greig, who was convicted of helping him while he was a fugitive for 16 years. The 1st U.S. Circuit Court of Appeals upheld a judge’s ruling to allow family members of Bulger’s victims to speak at her sentencing hearing. The court found that a sentencing judge has the right to conduct a “broad inquiry” when deciding an appropriate sentence.

“Thus, this court should exercise its broad discretion and permit all of the victims to speak at the upcoming sentencing hearing,” Assistant U.S. Attorneys Fred Wyshak Jr., Brian Kelly and Zachary Hafer wrote.

Bulger, now 84, was one of the nation’s most wanted fugitives after he fled Boston in 1994. He was captured in Santa Monica, Calif., in 2011.