"Darrent was a guy that was always upbeat, always had a smile and he was a fierce competitor," said Broncos coach Mike Shanahan, fighting back tears.
Williams was killed in a drive-by shooting early Monday, hours after the Broncos were eliminated from playoff contention.
"We're working around the clock on this investigation," police spokesman Sonny Jackson said.
"It's a situation where anyone who knows what happened or has any information, we'd love to hear."
Jackson said the police had not identified any suspects, and were unsure of the nature of the taunts that they believe sparked an altercation at a night club before the shooting that also wounded two other people.
Police were searching for a white Suburban or Tahoe with dark-tinted windows.
Williams sustained a single gunshot wound to the neck, according to Robert Whitmore, chief medical examiner in the county coroner's office.
The team will hold a private memorial Wednesday at Bronco headquarters so that Williams' teammates can tell his family what he meant to them.
The Broncos also will fly together to Fort Worth, Texas, for Williams' funeral on Saturday.
"He's in a better place right now," Shanahan said, choking up at a news conference.
"It's hard to understand right now. He's a good man. He's up in heaven right now."