Police say “hope is fading” to find Chris Baghsarian alive as investigations continue into an abandoned and “derelict” house where they believe the grandfather was kept sometime in the past week.

A warrant has been executed and a crime scene has been established at the semi-rural property on Wildthorn Ave in Dural, about 36km north-west of Sydney, after police swarmed the area on Thursday night.

The 85-year-old man has been held captive since three men bundled him into a dark-coloured SUV outside his Sydney home just before dawn last Friday.

Detectives previously said they believed the widower, who they say is a victim of mistaken identity, was alive after videos of him emerged restrained in an unknown location.

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Det Supt Andrew Marks told reporters on Friday there had been “significant progress in the investigation” and evidence obtained at the house suggested Baghsarian had been held there during the past week.

“Some good old fashioned police work with boots on the ground identified that location,” he said.

“It’s a vacant and derelict house, nobody lives there, it’s back from the street.

“We are appealing to people of Dural … have you seen something over the last seven days? Have you seen people that were coming and going from that address that does not fit that location?”

Marks said while police had been working “around the clock” they still hadn’t located Baghsarian or his kidnappers.

“That’s our main focus, to recover Mr Baghsarian and bring him home safely to his family … to get the medical treatment he requires,” he said.

“It’s been seven days now so hope is fading, we have grave concerns for his safety but we won’t give up trying to find him alive.

“I don’t know why [the alleged kidnappers] have left [the property], I don’t know why Mr Baghsarian is not there, we’re hopeful we can gain more evidence to identify those responsible and gain some information as to the location of Mr Baghsarian.”

Baghsarian’s family spoke publicly for the first time earlier this week, describing the kidnapping as a surreal and harrowing ordeal.

“Our family is living through a nightmare we never thought possible,” they said in a brief statement released via police.

Marks said he had spoken to the family overnight and the events had given them “a shock”.

“They’re anxious, they’re devastated and they want some answers,” he said.

“We are making inroads into this investigation and we really want to find Mr Baghsarian for them. We don’t know who is responsible so we’re after assistance from the public to give us information, no matter how small they think it is.”

Baghsarian’s lack of 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.

“It’s not an instance where they’re randomly taking people for the sake of it,” Marks told reporters on Monday.

“They were intending to take somebody but have taken the wrong person.”