Lonnie Franklin Jr., 58, has pleaded not guilty to the murders of 10 women over several decades. Most of the victims were found within several miles of his south Los Angeles home.
Deputy District Attorney Beth Silverman told a court her office will ask a jury for the state's harshest sentence if Franklin is convicted.
The announcement came as capital punishment is coming under increasing fire in California for lengthy delays in executions and for the expenses involved in winning cases, fighting appeals and keeping inmates on death row.
Last month, a state Senate bill that seeks to abolish California's death penalty advanced after its first legislative hearing in the Assembly. Now awaiting action in a committee, the bill would put the question before voters in 2012 if it is passed.
Franklin remains under investigation in several other killings.
In April, the LAPD said detectives are focusing on eight other women known to have had a connection to Franklin.
The Associated Press contributed to this report.