The Hala Akhbar site reported today that the attempted infiltration took place the previous day.
A statement attributed to security officials says border guards spotted seven men with six bags of hashish. It did not say how three of the men were killed.
The Syrian-Jordanian border is heavily guarded because of Jordanian concerns about the spillover from Syria's six-year-old civil war.
Jordan sealed the border last year, after a cross-border car bomb attack by Islamic State extremists killed seven Jordanian border guards.
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