A US federal court is close to imposing an antitrust remedy on Apple that narrows the scope to the company's e-book business.

US District Judge Denise Cote said in a Tuesday hearing that the remedies to price-fixing that Apple must take should be narrow and should not target Apple's content businesses other than e-books.

Cote struck language proposed by the Justice Department in the draft injunction that would have allowed scrutiny of Apple's sale of movies, music, television shows and other retail products.

The injunction will only cover e-books, she said. She hopes to finalize the injunction in the next week.

Cote, in a withering July 10 decision in the government's much-watched antitrust trial against Apple, concluded that Apple was liable for "facilitating and encouraging" a price-fixing conspiracy among publishers that cost consumers hundreds of millions of dollars.

An additional trial on damages is scheduled for May 2014.

Cote signaled that she wants to avoid excessive oversight of Apple while imposing remedies to the price-fixing.

"I want this injunction to rest as lightly as possible on the way Apple runs its business," Cote said, according to a transcript of the hearing.

"I want Apple to have the flexibility to innovate, but at the same time, I want to prevent a repetition of the illegal conduct like that shown with overwhelming evidence at this trial."

However, Cote said that while she initially resisted appointing an external monitor for Apple, she now viewed the step as necessary in light of Apple's "blatant and aggressive disregard" of the law as demonstrated by the trial. Apple's correspondence on antitrust compliance since the verdict has been "inadequate," she added.

"I have been reluctant to appoint a monitor for several reasons. But I believe based on the record before me now that I should," Cote said.

The purpose of the monitor will be to evaluate Apple's antitrust compliance policies and procedures, as well as to oversee its antitrust training program for staff.

Cote said all staff who work on content-related negotiations, whether on books, music, movies or other products, should receive antitrust training.

The training could be effectively executed in as little as 30 minutes for some employees, she said.

"The training needs to make an impression, to be memorable and to be helpful to an employee who wants to succeed for Apple and to do so within the bounds of the law," Cote said.