The 33-year-old, reportedly from Texas, was gunned down as he jogged in Benghazi's Fweihat district, the BBC reported.
He worked at an international school in Benghazi.
A security official said on Libyan television authorities have not determined the motive for the attack, the New York Times reported.
"The assassination of the American teacher is a continuation of a series of assassinations that the city is going through," the official said.
A person who claimed to be an eyewitness said the gunmen who shot Smith were driving a black Jeep.
A photograph circulating on social media purported to show Smith's body dressed in running clothes face down in a pool of blood. The authenticity of the photograph could not be verified.
The U.S. Embassy in Libya has not yet released a statement.
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