Judge Michelle Leavitt asked Thomas Richardson whether he wanted to speak to jurors before they went home Tuesday night.
"I don't know if it would make much of a difference at this point," he said.
The jury found the 42-year-old California man guilty of beating to death a 91-year-old cancer survivor and her grandson with a claw hammer.
The same jury will next decide whether he should be put to death for his crimes.
Authorities said Richardson came to Las Vegas over the 2005 Labor Day weekend with his girlfriend's teenage son, Robert Denhart, with a plan to rob and kill Steven Folker, 43. Folker was staying with his grandmother, Estelle Feldman.
After consulting his attorneys, Richardson did speak to the jury. In an even, conversational voice, he said, "I accept full responsibility for my actions of Sept. 7, 2005. As inadequate as it sounds coming from me, I apologize to the family for the loss of their loved ones. I truly do. There's nothing else I can say except that I am sorry."
The penalty phase of the trial is expected to finish today with closing arguments made by prosecutors and defense attorneys.
The jury will then decide how to punish Richardson for the two murders. The jury can choose capital punishment, life in prison without the possibility of parole or life in prison with the possibility of parole.
Today will be the third day of the penalty phase. Over the past two days, the jury heard about other crimes that resulted in convictions against Richardson, including the robbery of a Kmart in California he committed with Denhart in 2005.
Richardson was convicted in 1992 of raping a woman in San Antonio, Texas, while he was in the Army. Jurors heard directly from the victim of that case, who described the sexual assault in graphic detail.
Jurors also heard from multiple family members of the victims, who have watched the trial and penalty phase.
During almost 30 minutes of tearful testimony on Monday, Marchia LaFrance told the jurors how she lost both her mother and her son in one day. LaFrance also described how strong and independent her mother was at age 91 and how sweet and generous her son was.
"He gave the best hugs in the world," she said of Folker.
Feldman was her best friend and a 10-year colon cancer survivor when she was killed, LaFrance said.
"It was the most unfair thing in the world that these two innocent and wonderful, loving people are gone," LaFrance said. "I don't know how anyone, any human, could possibly do what was done to my mother, 91 years old, and my son, 43 years old. I just don't understand it."
Richardson's mother, El Louise Richardson, testified Tuesday that she loved her son.
Defense attorney David Schieck asked whether she would communicate with Richardson in light of his crimes. "Of course, he's my son," she said.
She testified that her husband and Richardson's father, a retired state trooper in Washington, died of cancer in June. Schieck asked why, with her recent loss, she came to testify. "He's my son, and I love him."
Denhart in July pleaded guilty to first-degree murder and robbery with use of a deadly weapon and testified against Richardson. In exchange, prosecutors will recommend Denhart receive a sentence of 24 to 80 years in prison.
Contact reporter Francis McCabe at firstname.lastname@example.org or 702-380-1039.