In a two-sentence statement today, family spokesman Barak Barfi said Sotloff's family, quote, "knows of this horrific tragedy and is grieving privately."
The family has not been told whether the video is authentic, and Barfi said the family does not plan to make any additional comments now.
Earlier, the State Department said U.S. Intelligence officials were still trying to determine if the video was genuine.
Sotloff had been held by the Islamic State since last year.
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