U.S. District Judge Denise Cote said in a written opinion that the deterioration of the relationship between Apple Inc. and the monitor was "unfortunate and disappointing."
But she said Apple had failed to show it was in the public interest to stop the work of a monitor put in place for two years after Cote concluded last summer that Apple disobeyed antitrust laws when it conspired with book publishers to raise electronic book prices in 2010.
"If anything, Apple's reaction to the existence of a monitorship underscores the wisdom of its imposition," she wrote. "A monitorship which succeeds in confirming the existence of a genuine and effective antitrust compliance program within Apple is in the interest of not only the American public but also Apple."
Cote's ruling explained why she told lawyers at a Monday hearing that she was rejecting Apple's request that she disqualify the monitor she appointed in the fall.
The judge said she hoped the relationship between Cupertino, Calif.-based Apple and the monitor, Washington lawyer Michael Bromwich, could be "reset and placed on a productive course."
An Apple spokesman did not immediately respond to a message for comment Thursday.
Bromwich, a former inspector general for the Justice Department, told Cote in a December court filing that he had encountered unprecedented obstacles in dealing with Apple when compared with his experiences in 20 years of doing oversight work, including three times before as a monitor and scores of investigations in the public and private sector.
Cote noted that Apple had turned over 303 pages of documents and permitted Bromwich over the last three months to conduct 13 hours of interviews with 11 people, seven of them lawyers.
"If this limited amount of access constitutes 'irreparable harm' to Apple then the standard for irreparable harm is low indeed," the judge said. She added that Apple appeared to have backed away from its claim that Bromwich was harming its market growth and product innovation.
In court papers, Apple had argued that Bromwich launched a "broad and amorphous inquisition" and was "conducting a roving investigation that is interfering with Apple's business operations, and imposing substantial and rapidly escalating costs on Apple that it will never be able to recover it if prevails on its pending appeal."
Cote showed little sympathy for the claims of potential financial consequences to Apple, which reported in September that it had $147 billion in cash.
Apple also had complained that it was "suffering from Mr. Bromwich's unwarranted inquisition of the company's high-level executives and board of directors" and said Bromwich had made a particular effort to interview former Vice-President Al Gore, an Apple board member.
But the judge said court papers showed only one instance when Bromwich sought to interview Gore. She said the request came because Gore was among three board members who the monitor believed were based near Apple's headquarters.
Cote praised Apple for recently hiring lawyers to help it create an improved antitrust compliance program, but she said the decision was "directly traceable to the creation of the monitorship."
Associated Press writer Michael Liedtke in San Francisco contributed to this report.