As community members sought emotional healing in the wake of the shooting spree at a religious service, police said Tuesday they had not identified a motive or found any telltale writings or note left by the gunman.
Oak Creek Police Chief John Edwards also said family members of Wade Michael Page, 40, have not reported observing any warning signs.
Page, an Army veteran who neighbors say played in a far-right punk band, was the lone gunman in the Sunday rampage at a Sikh temple, Edwards said. Page was shot to death by police responding to the attack.
According to Edwards and the FBI, authorities have received tips that Page might have links to the white supremacist movement, but nothing had been confirmed.
"We may end up with just a lot of facts on what he is involved with, who he may be associated with, but we may never know that motive, because he died, and that motive died with him," Edwards told CNN's "The Situation Room."
The chief also said, counter to speculation, Page did not have a 9/11 tattoo.
While the FBI has said Page never was the subject of an investigation, he was mentioned in a small number of federal law enforcement reference files in cases going back seven years, a law enforcement official told CNN on Tuesday.
The official said there is no information to suggest that investigators wanted to open a case on Page, but did not have the evidence to justify it. While Page might have been sympathetic to a certain ideology, there was no evidence he had committed a federal crime prior to the Wisconsin shooting, the official said.
The official did not provide details about the nature of the cases in which Page's name was mentioned.
For a third consecutive night, mourners and supporters held a vigil Tuesday night to remember the six victims, pray for the wounded and grapple with grief and shock.