The row covers technology used in iTunes, Time Machine and Spotlight
Apple has asked a court to reconsider an impending decision that could cost it more than $600m (£379m) in damages.
On 1 October, a US jury found in favour of Mirror Worlds in a
patent wrangle over technology to display documents on computer
screens.Mirror Worlds alleged that Apple had infringed four of its patents.
After weighing evidence the jury said three had been infringed and awarded the company $208.5m damages for each one.
Apple is asking for a delay to the judge's final decision saying there were unresolved issues with two of the three remaining patents in the case. If the court agrees damages will be reduced to $208.5m.
However, if the judge decides three patents have been infringed the damages award of $625.2m would be among the largest in US legal history.
In closing arguments made in the court and reported by the Bloomberg news agency, Apple said there were grounds for believing the patents were not valid and therefore whether they had been infringed.
It added that the patents had been sold and any damages awarded should reflect that market value. The patent package is believed to have been sold for $5m.
The row revolves around technology Apple has used in three products; Spotlight, Time Machine and Cover Flow. Two of the patents cover ways to display similar documents in a pile that users can then flick through.
Both Apple and Mirror Worlds have been asked to submit documents to the court concerning the damages ruling.
Mirror Worlds founder David Gelertner said he was "tremendously grateful" to his lawyers after hearing the verdict.
Apple has yet to respond to a request for comment on the case.