Chris Baghsarian, 85, has been held captive since three men bundled him into a dark-coloured SUV outside his Sydney home just before dawn on Friday.
While police are confident the grandfather and widower is still alive, videos of him restrained in an unknown location have prompted grave concerns for his safety.
His desperately worried family spoke about their harrowing ordeal for the first time on Tuesday.
"Our family is living through a nightmare we never thought possible," they said in a brief statement released via police.
"Chris's kidnapping feels surreal, and we are struggling to make sense of the fact that he has been taken and that our family has been caught up in something that has nothing to do with us."
They described him as a deeply loved and gentle family member "who would never hurt a fly" and asked for privacy as they navigated "an extraordinarily distressing time".
Vision published by Nine News shows a dark Toyota pulling into a street in North Ryde before Mr Baghsarian is abducted from his home.
A man in hi-vis clothing is seen emerging from the car, followed by an accomplice.
Moments later, they are seen pushing the elderly man across the landing as the car moves closer.
Police said a burnt-out vehicle matching the description of the SUV involved was found nearby.
Mr Baghsarian's lack of family or personal links to any criminal or underworld activity is making the case difficult for investigators.
No ransom has been demanded, leaving police to appeal directly to the kidnappers to return the grandfather to a safe location.
NSW Premier Chris Minns echoed calls for the perpetrators to release Mr Baghsarian but warned there would be serious consequences for the abductors once caught.
"It's not too late to end this situation ... please return him to his family," he said on Monday.
"Drop Mr Baghsarian off at a shopping centre, an emergency department or even a nursing home."
Police would not confirm if the intended target of the kidnapping had links to organised crime.
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