An Apple computer is shown on Google's company campus in Mountain View, California. Credit: Reuters/Robert Galbraith
Apple did not return telephone calls seeking comment and Google said only: "As we have said many times before, we will continue to vigorously defend our partners".
Google and Apple have been locked in an international patent war since 2010, as Apple has sought to limit the growth of Google's Android system. The fight has embroiled Samsung, HTC and others that use Android.
Reuters reported in August that the two companies were in settlement talks. Google said in its filing, however, that "there are no agreements between Motorola and Apple, written or oral, express or implied, concerning the subject matter of this investigation."
The complaint can be re-submitted.
Florian Mueller, who was first to report the withdrawal on his blog, said he believed that Google withdrew the complaint to prevent it from being consolidated with an earlier case, thus slowing that case down.
In that case, an ITC judge had said in a preliminary ruling that Apple infringed on a patent for eliminating noise and other interference during voice and data transmissions. A final decision is due next April.
"Maybe they ... wanted to maintain their chances of at least getting some win against Apple in the U.S. in 2013," Muller said in an email interview.
The biggest victory in the smartphone patent war so far belongs to Apple. On August 24, a jury in a California federal court ordered Samsung to pay $1.05 billion in damages after finding that Samsung had copied critical features of the iPhone and iPad.
Samsung was the top-selling mobile-phone maker in the second quarter of 2012, with Apple in third place, according to data from Gartner Inc.