Mr. Rivera, who repeatedly vowed that he wanted to be punished with death for raping and murdering 21-year-old Marni Glista, asked the Georgia Supreme Court on Thursday to reconsider his appeal.
On Monday, Mr. Rivera's attorney Peter Johnson said Mr. Rivera recently saw his children for the first time since he was sent to death row in 2004.
"He wants to live for them," Mr. Johnson said of Mr. Rivera.
He will file a petition with the U.S. Supreme Court asking it to consider an appeal on Mr. Rivera's behalf.
Late last month, the state's highest court affirmed Mr. Rivera's conviction and death sentence. A Richmond County Superior Court jury unanimously voted for death in January 2004.
Mr. Rivera was convicted of attacking Army Sgt. Glista in her Augusta home in September 2000. An officer sent to find out why Sgt. Glista hadn't reported for duty after the Labor Day weekend found her barely alive. She died several days later after doctors declared her brain dead and disconnected life support.
Mr. Rivera, 43, confessed to Sgt. Glista's murder, the slayings of three other young women on both sides of the Savannah River, and the attempted murder of an Augusta teenager on Oct. 10, 2000.
Mr. Rivera's confessions led investigators to discover the remains of two victims - 17-year-old Melissa Dingess in Aiken County and 17-year-old Tabitha Bosdell in Columbia County.
Melissa died July 17, 1999. Mr. Rivera told investigators that he next killed Tiffaney S. Wilson in Aiken County in December 1999 and Tabitha in June 2000.
Reach Sandy Hodson at (706) 823-3226 or firstname.lastname@example.org.