Apple seeks a path to getting 2 of its best watches back on shelves during a bitter patent dispute

Apple filed an emergency motion seeking court permission to begin selling two of its most popular watches again until a final decision on its broader appeal in a bitter patent dispute is decided.

The company cut off sales right before the Christmas holiday and in a motion filed Tuesday, Apple said it would suffer “irreparable harm” if previous court orders remain for the two weeks that it said the U.S. International Trade Commission will take to respond to its appeal.

The disruption will likely cost Apple about $300-400 million in...