The Defense Department is working with Elon Musk’s SpaceX to find and disable Starlink satellite internet terminals that have fallen into Russian hands, but the problem is not going away, a top Pentagon official said Tuesday.

SpaceX’s Starlink terminals enabled Ukrainian forces to communicate with each other and with their families after Russia’s 2022 invasion had shut down Ukraine’s internet and telephone services. But The Wall Street Journal reported in April that thousands of Starlink terminals have migrated to the black market, where Russia has obtained them and is using them to aid its operations in Ukraine.

Russia’s use of the system has reportedly slowed and disrupted the service for Ukrainians. Other U.S. foes and war criminals in the Mideast, Africa and Southeast Asia have also obtained the terminals, according to the report.

“Reports indicate that Russia has been able to buy Starlink terminals on the black market and that SpaceX has not cut off their access, and that provides a major advantage to Russia on the battlefield,” Sen. Elizabeth Warren, D-Mass., said at a Senate Armed Services Strategic Forces Subcommittee hearing on Tuesday.

Earlier this month, Warren wrote to Defense Secretary Lloyd J. Austin III seeking answers about the diversion of hardware from SpaceX, a U.S. defense contractor.

“Congress has a constitutional responsibility to make sure that taxpayer money does not go to companies that undermine U.S. national security goals,” Warren said at Tuesday’s hearing. “So I think it’s critical that we get to the bottom of this.”

John Hill, the deputy assistant secretary of Defense for space and missile defense, said in response to questions from Warren that the department is scouring classified and public data to find and shut down the terminals and suggested it has had some success. He said the push is partly led by a “commercial integration cell” composed of contractor and government personnel and located at the Combined Space Operations Center at Vandenberg Space Force Base in California.

But Hill could not provide any guarantees about the extent to which the cat-and-mouse initiative would succeed in addressing the problem. When Warren asked Hill if he has confidence the Pentagon can “identify illicit Russian use of Starlink services and completely shut them off,” Hill responded, “I think this will be a continuous problem.”

To that, Warren replied, “I take that as a no.”

Hill assured Warren that SpaceX has been “cooperative” and “forward leaning” in assisting the search for illicit Starlink terminals.

“SpaceX complies with our contracts, and they comply with the licenses they have from regulatory entities who can enforce those licenses,” Hill added.