The assessment came in the first report issued by the monitor, Michael Bromwich, who found himself the subject of a bitter fight by Apple to put his work on hold while it pursues an appeal.
In a 77-page report filed in U.S. District Court in New York, Bromwich said the relationship between his team and Apple has "significantly improved" since a federal appeals court in February rejected the iPhone maker's bid to halt his work.
But Bromwich said while progress had been made in enhancing Apple's antitrust compliance program as ordered by U.S. District Judge Denise Cote, his team has only been able to speak with a limited number of company employees.
The monitoring team has been unsuccessful in speaking with senior members of Apple and "still lacks a significant amount of the information it needs to fulfill its monitoring obligations," he said.
"Based on the information Apple has provided to date, our view is that Apple has made a promising start to enhancing its antitrust compliance program, but that Apple still has much work to do," Bromwich wrote.
A lawyer for Apple declined comment. A spokeswoman for the U.S. Justice Department did not immediately respond to a request for comment.
Bromwich, a former Justice Department inspector general, was appointed by Cote as monitor in October, three months after she found the company liable in the civil antitrust case.
The judge had in July found that Apple played a "central role" in scheming from late 2009 into early 2010 with five publishers to raise e-book prices and impede competitors such as Amazon.com Inc.
The publishers previously agreed to settle with the Justice Department and pay more than $166 million to resolve related states attorneys general lawsuits and consumer class actions.
The publishers included Lagardere SCA's Hachette Book Group Inc, News Corp's HarperCollins Publishers LLC, Penguin Group (USA) Inc, CBS Corp's Simon & Schuster Inc and Verlagsgruppe Georg von Holtzbrinck GmbH's Macmillan.
Apple had fought against Bromwich being able to carry on in his role as monitor, contending he aggressively and improperly sought interviews with top executives and broad access to company documents.
But in February, the 2nd U.S. Circuit Court of Appeals in New York rejected Apple's bid to put the monitor on hold.
In the wake of that ruling, Bromwich said "there has been a shift of tone in our relationship with Apple," and Apple has demonstrated "a greater commitment to resolving lingering disputes."
The report said Apple has fulfilled a requirement by Cote to appoint an internal antitrust compliance officer, hiring Deena Said, a former in-house attorney at Hitachi Ltd.
But Bromwich said Apple needs to take further steps to achieve the court's goals, including improving its record-keeping procedures and provide more information related to training of its personnel.
Apple continues to challenge the monitor's activities at the appellate level. It is also appealing the liability finding as it faces a July 14 trial on damages. Lawyers for the plaintiffs say they are entitled to $840 million.
The company sought permission late Monday to appeal a order by Cote last month granting class certification in the consumer class action.The consolidated case is In Re: Electronic Books Antitrust Litigation, U.S. District Court for the Southern District of New York, No. 11-md-02293.