DNA evidence has now linked Woodward to the crime.
David Thalberg, a spokesman for the Bernstein family said: "We want people to do acts of kindness". He is accused of killing Bernstein and burying his body in a shallow grave in the park.
Bernstein's body was found Tuesday after recent rains partially exposed it. A memorial of balloons and flowers, left, was placed on a table near the site.
After the discovery of Bernstein's body, Woodward was arrested and is expected to make his first appearance in court on Wednesday.
The death rocked the community, where hundreds of people held a candlelight vigil to remember him.
Orange County School of the Arts High school yearbook senior tribute to Blaze Bernstein.
Witnesses said he was last seen at approximately 11 p.m the night before, entering Borrego Park in Foothill Ranch with a friend.
Bernstein was reported missing on January 3 by family-they were anxious after he didn't show up for a dentist appointment and his wallet and glasses were still in his bedroom.
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The 20-year-old suspect arrested for the murder of 19-year-old University of Pennsylvania student Blaze Bernstein reportedly posted about guns and waterboarding online, writing that if he was stranded on a desert island, he would bring with him only "The Bible and a Colt.45".
The murder weapon has not been found, according to reports.
Woodward also told investigators that Bernstein walked into the park alone and that he waited for an hour before driving to meet with a girlfriend, the newspaper reported.
Blaze's lifeless body was found on January 9, just outside Borrego park, the last place Woodward claimed he saw him. He said he returned to the park hours later to look for Bernstein. Woodward was allegedly "unable to provide his girlfriend's last name, phone number or address", when questioned by investigators.
Woodward was arrested Friday after crime lab technicians determined that blood found on a sleeping bag in his possession belonged to Bernstein, the Register learned.
Bernstein may have been planning to sexually pursue Woodward, according to a 16-page search warrant affidavit obtained by the Register.
Bernstein reportedly claimed that Woodward "made me promise not to tell anyone ... but I have texted every one, uh oh". The affidavit also noted that Woodward told investigators that Bernstein kissed him on the lips, and that he pushed Bernstein away.
As he recounted that part of his story, Woodward clenched his jaw and his fists, saying "he wanted to tell Blaze to get off of him", investigators wrote.
Police zeroed in on Woodward as a person of interest when they noticed he had scratches on his hands and dirt under his fingernails. He continued, "How well they were friends in high school we do not know".
Leading up to the death, Woodward's social media content had become increasingly violent and included defenses of the confederate flag.