"As the principal, I offer my apology for these errors in judgment," she wrote.
The school, with a student body that's more than 90 percent Hispanic, will work with the district's Office of Human Relations, Diversity and Equity to help students and adults learn from the experience, the letter said.
A call to Abner seeking further comment was not immediately returned.
During a Feb. 26 parade in the school playground honoring Black History Month, some youngsters carried photos of Simpson, RuPaul and Rodman while others displayed more conventional role models such as President Barack Obama and the Rev. Martin Luther King Jr.
Simpson, a former NFL star, is serving a nine-year prison sentence for robbery and kidnapping in Nevada. He was acquitted in 1995 of murdering his ex-wife and her friend.
RuPaul is a drag queen performer. Rodman, a former basketball star, has gained notoriety for bad boy behavior.
Three teachers – all white men who teach first, second and fourth grades – were suspended without pay for three days and are now on paid administrative leave while the Los Angeles Unified School District investigates the incident, district spokeswoman Gayle Pollard-Terry said.
Their names have not been released.
The district is investigating "why the teachers believed these were appropriate instructional choices for first-, second- and fourth-graders," Pollard-Terry said, adding that she did not know how long the investigation might take.
Simpson's name was included on a sign-up sheet that had a list of figures approved for Black History Month activities, but the list dated back to 1985, Pollard-Terry said.
The list had 60 printed names, including Simpson. A handful of teachers added other names in pencil.
Those included RuPaul and Rodman as well as Obama, Colin Powell, Miles Davis and others, the district spokeswoman said.
"The principal never saw the list, so that's why it wasn't school-approved," Pollard-Terry said. "I'm trying to find out who passed the list out."
Superintendent Ramon Cortines has called the incident a failure of oversight by the principal, who was not on campus during the parade.
The principal has accepted responsibility as well and could face discipline, Pollard-Terry added.
The issue was brought to the attention of district officials by the Los Angeles chapter of the National Association for the Advancement of Colored People after the organization received a complaint Monday.