Los Angeles (CNN) -- Slain Santa Monica gunman John Zawahri left behind a note on his body apologizing for killing his father and his brother and hoping his father's estate would support his mother, police said Friday.
Zawahri, 23, who lived with his father in a house that was also set afire, wrote a three- to four-page handwritten letter in which he spent a "larger" measure of it saying good-bye to his friends than talking about his family, police said.
Authorities described the tone of the letter as "conversational talk" without "overall hatred to anything," a police spokesman said.
"He was sorry for having killed his father. He was sorry for having killed his brother, that he hoped his mother would be looked after financially and that she would receive financial recompense from the father's estate, and he said goodbye to his friends," said Santa Monica Police Chief Jacqueline Seabrooks said.
"It was more of a farewell," Seabrooks added.
No motive to his alleged shooting -- in which a total of five people were killed -- was given in the note, she said.
Police revealed Friday that Zawahri tried a buy a weapon in 2011, but the U.S. Justice Department issued a notice stating that Zawahri was ineligible to buy a firearm.
Seabrooks said the Justice Department denial "may have something to do with our contact with him in 2006, but I'm not sure."
Police had contact with Zawahri in 2006, but because he was a juvenile then, authorities weren't releasing further information, the chief said.
Zawahri had suffered mental health issues, a law enforcement source with knowledge of the investigation told CNN last week. A couple of years ago, he was hospitalized for treatment after allegedly talking about harming someone, according to the official.
It's not clear whether the California state government or his family committed him for treatment or whether he committed himself. It's also unclear under what circumstances he was released.
Zawahri used firearm components to construct a rifle that is illegal to possess, Seabrooks said Friday.
He allegedly fired 100 or fewer rounds during a shooting rampage across Santa Monica, adjacent to Los Angeles, that ended at the Santa Monica College, where police shot him to death, authorities said.
He was armed with multiple guns and about 1,300 rounds of ammunition, police said.
When asked where or how Zawahri obtained the firearms used in the shootings -- especially after the Justice Department deemed him ineligible to buy weapons -- Santa Monica Police Sgt. Richard Lewis stated: "That is a part of the investigation that we will not disclose."
His father and brother died of gunshot wounds, and their bodies were found in the back of the father's Santa Monica house, a police spokesman said. Their bodies were identifiable, "and it's not that they were burned beyond recognition," the chief said.
Neighbors said the parents were divorced. The mother has spoken with investigators, but the police chief didn't elaborate further.
Zawahri was unemployed and hadn't attended Santa Monica College, where his shooting rampage ended, since 2010, a police spokesman said Friday.
Gunman previously hospitalized for mental health