The individual, who allegedly used pepper spray in the incident, is described as a man in his 30s who wore black attire and rainbow-colored shoes, according to the LAPD.
The confrontation was reported around 10:45 p.m. Thursday at the intersection of Western Avenue and Olympic Boulevard, according to the Los Angeles Police Department.
When the officers arrived, they learned that two men had been involved in an argument and at some point one of the men pepper-sprayed the other man and then ran off the bus, police said.
Paramedics from the Los Angeles Fire Department were called to the scene and pronounced the 63-year-old man dead.
LAPD West Bureau Homicide detectives "are seeking to speak with the other individual involved in the altercation," a statement said. "This individual ... did not stay at the scene to meet with law enforcement."
In a statement, Metro said both of the men were passengers and that the official cause of death was unknown.
"Metro is working closely with the Los Angeles Police Department as they investigate this incident. Safety is our number one priority and over the past year Metro has seen an overall, month-over-month reduction in serious crimes on our transit system due to our multilayered public safety plan, which includes the addition of Transit Security Officer and law enforcement bus riding teams on key Metro bus lines. However, one crime is too many and will not be tolerated."
Pepper spray is known as a non-lethal form of defense. A police detective at the scene told ABC7 that the Los Angeles County medical examiner would determine how exactly the 63-year-old man died.
Anyone with information about the altercation was urged to call the LAPD's West Bureau Homicide at 213-382-9470 or 877-527-3247. Tipsters may also contact Crime Stoppers at 800-222-8477 or www.lacrimestoppers.org.