The military equipment had been shipped into Jordan as part of the Central Intelligence Agency's secret program to train and equip moderate Syrian rebels to fight troops loyal to Syrian President Bashar Al-Assad, The New York Times and Al Jazeera reported.
Citing unnamed American and Jordanian officials, the Times and Al Jazeera reported today that some of these weapons were used in a November shooting at a police training facility in Amman.
The Times and Al Jazeera said the FBI has been investigating the case for months.
The stolen weapons include Kalashnikov assault rifles, mortars and rocket-propelled grenades and the black market is newly awash with arms, the reports said.
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Investigators aren't sure what happened to most of the weapons but many are likely to have ended up in the hands of rural Jordanian tribes, criminals or shipped to other countries.
The FBI and CIA declined to comment.
Arab intelligence services and the CIA have been training rebels since 2013 under the code name Timber Sycamore. The training effort is run from Jordan because of its proximity to Syria.
Though the program is classified, officials told the Times and Al Jazeera that the CIA has trained thousands of rebels in the past three years.
The fighters had been making progress against Syrian regime troops until Russia joined the war last year on Assad's side.