Arnold Mouat was last seen at a property in Panbrae Road, Bo'ness at about 23:30 on 6 July.
Mr Mouat subsequently left the address at some point during the night and has not been seen since.
Police officers will be in Bo'ness on Friday to speak to people who may have been in the area on 7 July.
In a statement issued through Police Scotland, Mr Mouat's family said:  "We're overwhelmed by the support shown by the local and wider community and are extremely grateful to everyone who has offered to help find Arnold.
"This includes the volunteers who assisted the police with searches yesterday morning and afternoon."
Mr Mouat's family said it had been "a very difficult time for all of us".
The statement continued: "We ask anyone who has information that might assist police with their ongoing search effort to please make contact immediately.
"Likewise, Arnold, if you're reading this then please let us know that you're okay."
A public search of the Bo'ness area attended by 59 volunteers was carried out on Thursday.
Police said local and specialist resources had been deployed across Forth Valley, West Lothian and South Queensferry.
Mr Mouat is white, about 6ft 3in tall, with dark receding hair, a tanned complexion, and speaks with a Shetland accent.
He is believed to be wearing distinctive blue running trainers, but the rest of his clothing is unknown.
Insp Jim Young said:  "I'd like to pay tribute to Arnold's family who have shown incredible strength during what is undoubtedly a very difficult time.
"I would also like to thank the public for their assistance throughout this investigation, their support has been crucial.
"Unfortunately we are still looking for that key piece of information that will lead to us finding Arnold and give us the answers his family are desperately seeking."
The family of a 64-year-old man who has been missing for a week say they have been "overwhelmed" by support from the public.