SAN FRANCISCO—A federal judge overseeing a whistleblower lawsuit against Gilead Sciences Inc. seemed on the verge of granting a request from government lawyers to dismiss the long-running case Thursday afternoon, but stopped just short. 

U.S. District Judge Edward Chen of the Northern District of California said the level of scrutiny he would give to the government’s decision to ask to dismiss the case was “very low.” But Chen said he wants to give the government lawyers an opportunity to provide further detail about their basis for asking to dismiss the case, where two former Gilead employees claim the company illegally charged the government hundreds of millions of dollars for tainted HIV drugs.