Gilead Sciences shares popped by more than 8% on Friday after details leaked of a closely watched clinical trial of the company's antiviral drug remdesivir, showing what appears to be promising results in treating Covid-19.

The University of Chicago's phase 3 drug trial found that most of its patients had "rapid recoveries in fever and respiratory symptoms" and were discharged in less than a week, health-care publication STAT News reported Thursday.

"The best news is that most of our patients have already been discharged, which is great. We've only had two patients perish," University of Chicago infectious disease specialist Kathleen Mullane said, according to STAT News, which obtained a video of her remarks.

Gilead shares jumped as much as 16% in after-hours trading Thursday immediately after the report published.

Gilead didn't immediately respond to a request for comment.

In a statement to CNBC, a University of Chicago spokesperson said, "Partial data from an ongoing clinical trial is by definition incomplete and should never be used to draw conclusions about the safety or efficacy of a potential treatment that is under investigation."