SAN JOSE—The federal judge overseeing the criminal case against Theranos founder Elizabeth Holmes stopped short of granting a request from her lawyers at Williams & Connolly to force the prosecution team to hand over potential defense-friendly evidence held by government agencies.

But at a hearing on the defense motion Friday, U.S. District Judge Edward Davila of the Northern District of California indicated that if the agencies ultimately withhold material requested by Holmes’ lawyers, he’s likely to issue an order compelling them to pony up.