Fayaz, who officials said remained hospitalized in grave condition on Tuesday, agreed to meet Jones on Saturday to buy a car for $24,000, Essig said.
Fayaz arrived with his brother-in-law, and Jones asked "jokingly" if the men were armed, Essig said. Jones then put Fayaz in a headlock and demanded the money, the chief said.
An attempted robbery suspect in off-duty NYPD officer shooting was arrested at a motel. The off-duty officer met the man to potentially buy a car from him from Facebook marketplace.
Fayaz said he didn't have the money, Essig said, and Jones pointed a gun at Fayaz's brother-in-law. Fayaz broke free from the headlock and Jones shot him in the head, Essig said.
Jones ran, firing more shots at he fled, Essig said. The brother-in-law grabbed Fayaz's gun from his hip and fired several shots as well, he said.
Jones drove off in a 2011 BMW that was registered to his mother, Essig said.
Jones was arrested Monday at a Days Inn in Nanuet, about 35 miles north of New York City. A woman and five children ages 6 months to 11 years were with him at the motel, Essig said.
Charges against Jones were pending Tuesday. Information on his attorney was not available.