Just two weeks after the International Trade Commission voted to investigate Apple on patent infringement claims brought by the Google-owned Motorola Mobility, Motorola has dropped its complaint.

Motorola had asked for import bans on just about every notable Apple hardware product, including all Macs, iPads, and most iPhones. But the company completely dropped its complaint in a very short filing made with the ITC on Monday night.

“Complainants Motorola Mobility LLC, Motorola Mobility Ireland, and Motorola Mobility International Limited (collectively, 'Motorola') hereby move to terminate all claims in this investigation without prejudice based on Motorola’s withdrawal of the complaint, with Motorola and Apple each bearing their own costs and attorneys’ fees,” the filing states.

Apple and Motorola are pursuing various lawsuits against each other, including another suit Motorola filed against Apple in the ITC in 2010. That one is still active. While an administrative law judge ruled a Motorola patent is invalid, the full ITC disagreed. The case was sent back to the judge, and he wrote in a filing yesterday that he is targeting an April 2013 finish date.

Neither of the latest filings make reference to the other case, so Motorola dropping its newer complaint remains unexplained. Earlier in the day, Apple made its own filing asking for a 30-day extension on a deadline for responding to Motorola’s complaint due to “the complexity of this matter.” Motorola’s filing to drop the whole case was received by the ITC just a half hour later. Motorola did not specify why it’s dropping the complaint, but it did say there’s no settlement. “There are no agreements between Motorola and Apple, written or oral, express or implied, concerning the subject matter of this investigation,” Motorola said.

Not surprisingly, Apple confirmed to Motorola that it does not oppose the motion to drop the case. We’ve contacted Google, Motorola, and Apple to find out what spurred this latest move, and will provide an update if we receive one.