Saif al-Islam, Gadhafi's second son, was wounded in the leg by rebels and transferred to a hospital in Misurata, where he died soon after, the Post said.
Another Gadhafi son, Mutassim, was reported killed earlier, leaving the most active military elements of the family dead, the newspaper said.
National Transitional Council officials said Jabr was killed at the time of Gadhafi's capture.
Three other sons have reportedly fled Libya -- Saadi to Niger and Muhammad and Hannibal to Algeria, along with Gadhafi's second wife, Safiya, the Post said.
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