In a court filing in California, Apple said the smartphones and tablets were found to have violated patents in a jury trial held last year.
Apple renewed its bid for a permanent injunction on sales of a number of Samsung products after an appeals court decision last month cleared the way for a new hearing on the matter.
In the latest filing dated yesterday, Apple's attorneys wrote that the court "previously concluded that Samsung's sale of infringing products has irreparably harmed 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 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.
