A US jury on Tuesday condemned self-described white supremacist Dylann Roof to death over the massacre of nine black worshippers in a South Carolina church in June 2015 ─ a crime that shocked America.

Roof, 22, was convicted last month of 33 federal charges ─ including hate crimes resulting in death ─ in connection with the shooting spree at the historic Emanuel African Methodist Episcopal Church in downtown Charleston.

A Bible study group at "Mother Emanuel," which had welcomed Roof, was just beginning its closing prayer when the self-avowed Nazi and Ku Klux Klan sympathiser opened fire, killing nine people ranging in age from 26 to 87.

The slayings once again exposed the deep divides in America over race and access to guns.

Roof showed little reaction to the decision, delivered just hours after the 12-member jury retired to deliberate, though he occasionally seemed to be slightly smiling.

Federal judge Richard Gergel will formally deliver Roof's sentence on Wednesday morning at the Charleston courthouse. The verdict unanimously reached by the jury is binding.

"I still feel like I had to do it," Roof told jurors earlier in a semi-coherent closing argument.

Roof represented himself in the sentencing phase of the trial, against the advice of his lawyers and the judge. He called no witnesses and offered no evidence for the jury to consider.

After the jury offered its sentencing verdict, Roof asked for new attorneys so he could move for a retrial, but Gergel told him to provide specific reasons for his request on Wednesday.

Relatives of the victims will be invited to speak at Wednesday's hearing.

'Not one tear'

Earlier, prosecutor Jay Richardson urged jurors to sentence Roof to death for "this cold, calculated, malicious killing."

"Not one tear did he shed for those that he killed," he said. "Unrepentant. No remorse."

Richardson noted Roof only expressed sorrow that he put his parents through an emotional trial during which his mother suffered a heart attack after a survivor's gripping testimony.

"He had sorrow for them. He had pity for himself. That he had lost his freedom. His ability to watch movies and drive a car," he said. "But his sadness was reserved for the little white children that have to live with African Americans."

During the first phase of the trial, Roof exhibited no signs of remorse as survivors recounted the rampage in heart-rending detail.

A video of Roof's chilling confession was shown to the jury.

"Somebody had to do something because black people are killing white people every day," Roof said without emotion to the FBI special agent questioning him. "They rape 100 white people a day."

In notes confiscated from Roof in prison in August 2015, he wrote that he was "not sorry."

"I have not shed a tear for the innocent people I killed," the notes said.

Roof's lawyers had suggested their client was not mentally fit, but Gergel found Roof competent to stand trial ─ twice.

His family said in a statement posted in US media Tuesday that they would "continue to pray for the Emanuel AME families and the Charleston community."

"We will struggle as long as we live to understand why he committed this horrible attack, which caused so much pain to so many good people," the statement said.

US Attorney General Loretta Lynch, who is herself black, said in a statement that "we hope that the completion of the prosecution provides the people of Charleston ─ and the people of our nation ─ with a measure of closure."

Tim Scott, one of South Carolina's two senators, added that "nineteen months ago, a heartless murderer attempted to start a race war."

"Today that man was rightly sentenced to death," said Scott, who is black.

Capital punishment is only rarely meted out in federal cases, in part because violent crimes more typically are tried under state laws.

Federal authorities have executed only three inmates since 1976.

Roof is also facing state murder charges in South Carolina, and prosecutors were planning to seek the death penalty, but those proceedings were indefinitely put on hold last week.