The man convicted of murdering nine black churchgoers in South Carolina has told jurors that he was not mentally ill at the time of the shooting.

Dylann Roof has spoken to the jury for the first time at his death penalty trial, telling the panel there is nothing wrong with him psychologically.

He did not ask jurors to spare his life or the death penalty.

Dylann Roof in court

The jury last month unanimously found Roof guilty of hate crimes over the shooting deaths of nine black church members during Bible study in Charleston.

They will now decide whether he should be sentenced to death.

"My opening statement is going to seem a little bit out of place," the soft-spoken 22-year-old white man said calmly as he stood in front of a podium, occasionally glancing at notes.

"I am not going to lie to you ... Other than the fact that I trust people that I shouldn't and the fact that I'm probably better at constantly embarrassing myself than anyone who's ever existed, there's nothing wrong with me psychologically."

Prosecutors want Roof to face the death penalty because he deliberately chose to target vulnerable people during Bible study at Emanuel AME Church in June 2015.

"This defendant's horrific acts justify the death penalty," Assistant US Attorney Nathan Williams said.

"He killed nine people ... He killed them because of the colour of their skin. He killed them because they were less than people."

Mr Williams told jurors they would hear extensive testimony about the nine victims, including pastor and state senator Clementa Pinckney, a "prodigy of the ministry" who was a man of faith, service and family dedication.

"This will be heartbreaking," Mr Williams said.

The prosecutor also read a portion from a journal found in Roof's jail cell six weeks after his arrest in which Roof said he had not wept for any of the victims.

"I remember how I felt when I did these things and how I knew I had to do something and then I realise it was worth it," Roof wrote, as a handwritten page from his journal appeared on screens in the courtroom.

"I would like to make it crystal clear. I do not regret what I did. I have not shed a tear for the innocent people I killed."

Roof has said he does not plan to call any witnesses or introduce any evidence.