Koh didn't specify how much of the award she might cut, saying she would rule later on a host of legal demands made by both companies.
Samsung wants to overturn an August 24 jury verdict that found the South Korean tech titan ripped off Apple Inc.'s designs for its iPhone and iPad. The jury ordered Samsung to pay Apple $1 billion after finding about two dozen products used technology controlled by Apple.
Samsung is seeking a new trial while Apple is looking to add $500 million more to the award while barring many of the older Samsung products at issue from sale in the United States.
The case is ultimately expected to land before the US Federal Circuit Court of Appeals, the Washington, DC-based court that decides patent disputes, if not the US Supreme Court.
Nonetheless, what Judge Koh decides after Thursday's hearing will greatly shape the end result.
Samsung has mounted an aggressive post-trial attack on the verdict, raising a number of legal issues that allege the company was treated unfairly in a federal courtroom a dozen miles from Apple's Cupertino headquarters.
Samsung alleges that some of Apple's patents shouldn't have been awarded in the first place and that the jury made mistakes in calculating the damage award.