The Justice Department on Friday moved to drop charges against a Temple University professor accused of trying to send sensitive superconductor technology to China, a setback in the U.S. government’s push to become more aggressive with China over economic espionage.

The dropped charges come as the Federal Bureau of Investigation and the Obama administration have been ramping up efforts to counter what they say is a growing problem of economic espionage directed at U.S. companies by Chinese firms.

The...