The family of George Lindemann, a collector and philanthropist, returned the statues after conceding that they had been looted, Cambodian officials said.
Some experts believe this 17th-century work now up for sale was originally stolen by the Nazis, but no clues to its prewar owner have turned up in years of searching.
After it fired a worker for theft and its director stepped down, the museum faces renewed calls to give back contested objects and an uphill battle to raise funds for refurbishment.
The Manhattan district attorney’s office said the headless bronze, valued at $20 million, is a depiction of the Roman emperor and was looted from Turkey.