WASHINGTON — Federal authorities are investigating dozens of new cases of possible opioid and other drug theft by employees at Veterans Affairs hospitals, a sign the problem isn’t going away as more prescriptions disappear.

Records show 36 criminal investigations opened by the VA inspector general’s office from Oct. 1 through May 19. It brings the total number of open criminal cases to 108 involving theft or unauthorized drug use. Most of those inquiries typically lead to criminal charges.

The numbers are an increase from a similar period in the previous year. The VA has pledged ‘‘zero tolerance’’ in drug thefts after an Associated Press story in February about a sharp rise in reported cases of stolen or missing drugs at the VA since 2009.

Doctors, nurses, or pharmacy staff in the VA’s network of more than 160 medical centers and 1,000 clinics are suspected of taking controlled substances for their own use or street sale — sometimes to the harm of patients — or drugs simply vanished without explanation.

Drug thefts are a growing problem at private hospitals as well as the government-run VA as the illegal use of opioids has increased in the United States.

But separate data from the Drug Enforcement Administration obtained by the AP under the Freedom of Information Act show the rate of reported missing drugs at VA health facilities was more than double that of the private sector.

DEA investigators cited in part a larger quantity of drugs kept in stock at the bigger VA medical centers to treat a higher volume of patients and for distribution of prescriptions by mail.

Senator Marco Rubio, Republican of Florida, said AP’s findings were ‘‘troubling.’’ He urged Congress to pass bipartisan accountability legislation he is cosponsoring that would give the agency ‘‘the tools needed to dismiss employees engaged in misconduct.’’ The Senate is scheduled to vote on the bill June 6.

In February, the VA announced efforts to combat drug thefts, including employee drug tests and added inspections.