Mr MacKay, 61, was last seen leaving a house in the South Bragar area in the early hours of July 6.
He was wearing black boots, blue jeans and a navy blue hoodie.
Coastguard and mountain rescue teams are involved in the search coordinated by Police Scotland.
Constable Gary Muir, based in Stornoway, said: "We're appealing to people in the local area to contact us if they see Gordon or have any information about where he might be.
"Our search is ongoing and involves the coastguard and mountain rescue team as we do everything we can to find Gordon.
“The police and multi-agency search is coordinated and structured so I would ask people not to get involved in that, however I would ask people to check their sheds and outbuildings."
If you have any information on Mr MacKay’s whereabouts you should contact Police Scotland on 101 quoting incident number 3761 of July 6.