Siti Amirah, 83, was one of 44 Malaysians on board the Malaysia Airlines flight that was downed on Thursday killing all 298 people on board.
"I personally share the grief of the families on board #MH17," Najib said in a Tweet as quoted by Reuters. "My step-grandmother was one of the passengers."
Family spokesman Faridah Abdullah told the Star newspaper Siti "was a very, very nice lady".
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