Jerry Roberts, who was the top editor when he left the paper in July with other employees amid a feud with Publisher Wendy McCaw, denied any involvement in downloading the images. He has not been charged.
In a statement, Roberts called the article "outrageous, false and defamatory."
His attorneys said in a letter sent to News-Press attorneys that Ampersand Publishing LLC, which owns the paper, faced "imminent legal action seeking massive damages" if the story published Sunday were not retracted.
No retraction had appeared by Wednesday.
"We are assessing our options," said Andrine Smith, a lawyer for Roberts.
Attorney Barry Cappello, who represents Ampersand, defended the article, saying the company was concerned that a crime had been committed.
"Our interest is to determine who did it," Cappello said. "Some employee committed a crime on company property."
Police said it was difficult to determine who downloaded the "substantial" number of images featuring children and adults.
"It's our belief this computer had multiple owners," Santa Barbara police Lt. Paul McCaffrey said, adding the computer was not protected by a password.
The Police Department has asked the FBI to assist in retrieving further information from the hard drive.
The district attorney's office declined to comment.
The unbylined article said numerous computers were examined after several top editors, including Roberts, left the newspaper amid claims that McCaw had meddled in news coverage.
Roberts was the only person named in the story as a user of the computer containing the images.
Dozens of editors and reporters have either quit or been fired from the newspaper since last summer. McCaw has argued that some had injected their personal views into news coverage.
McCaw and Roberts have filed legal claims against each other. McCaw is seeking $25 million against Roberts for breach of contract, while Roberts wants $10 million in damages.
The 41,000-circulation daily is also the subject of an unfair labor practices investigation initiated by the National Labor Relations Board after newsroom employees voted 33-6 in September to unionize.
By: An editor who resigned from the Santa Barbara News-Press in a power struggle with the publisher is demanding a retraction of a front-page story that said a computer he had used at the office contained child pornography.