In the latest filing dated Thursday, Apple's attorneys wrote that the court "previously concluded that Samsung's sale of infringing products has irreparably harmed Apple."
The document added that the appeals court decision "makes clear that the record evidence collectively demonstrates a sufficient 'causal nexus' between Samsung's infringement and the irreparable harm to Apple."
Apple added that "money damages are not an adequate remedy for Samsung's infringement of these patents."
The US firm is seeking a ban on Samsung's smartphone models Captivate, Continuum, Droid Charge, Epic 4G, Exhibit 4G, Fascinate, Galaxy Ace, Galaxy Prevail, Galaxy S, Galaxy S 4G, Gem, Indulge, Infuse, Mesmerize, Nexus S 4G, Replenish, Vibrant,Transform and three versions of the Galaxy S II.
Bans are also being sought on the Galaxy Tab and Tab 10.1 tablets.
The request does not affect the newest Samsung devices, which were not at issue in the trial because of the fast product cycles in the industry.
The South Korean firm, the world's biggest maker of smartphones, has been ordered to pay Apple more than $900 million after a retrial on some of the issues in the case.
But the case, one of several being played out in courts and administrative agencies around the world, has not dented sales of Samsung, which has vaulted ahead of Apple in many markets around the world.