Apple sought the ban on Friday when it moved a paper in the federal court in California.
Devices added to a complaint Apple filed against Samsung in February were the Galaxy S III and its special Verizon edition; Galaxy Note; Galaxy Note 10.1 tablet; and the Galaxy S II in both its basic and carrier-independent forms.
The latest move by Apple comes at a time when there are thick rumors about Google Inc Chief Executive Larry Page and Apple CEO Tim Cook having conducted behind-the-scenes talks about a range of intellectual property matters, including the mobile patent disputes between the companies.
A Reuters report on Friday indicated at discussions involving lower-level officials of the two companies.
The February case has already resulted in a ban on the sale of Galaxy Nexus phones in the United States, although that injunction is pending appeal. Apple is seeking a similar ban against the Galaxy S III and other devices in its amended complaint filed Friday with the court.
(With inputs from Reuters)