Daniel McSwiggan, 69, was last seen in Almada Street, Hamilton, South Lanarkshire, on Thursday September 12.
Specialist police units including dogs, search teams and a helicopter have been involved in the search for him.
Police said they have had a good response to appeals from the public but have yet to find Mr McSwiggan and are concerned for his safety.
He is 5ft 7ins and bald with grey hair at the sides and has a moustache. When he was last seen he was wearing a dark-coloured jacket, dark grey trousers, a dark blue v-neck jumper, blue shirt and black shoes.
Inspector Alistair Anderson said: "Mr McSwiggan's disappearance has been widely publicised and the response from the public has been very good, but unfortunately his whereabouts are still unknown.
"Concern for his safety grows with each day that passes and his family are completely distraught.
"The last confirmed sighting we have is at 6.40pm on Thursday September 12 in Almada Street, Hamilton near to Hamilton Sheriff Court.
"Mr McSwiggan is seen on CCTV crossing the busy road and trying to get on a bus which was stationary at traffic lights.
"He was thereafter seen walking on Almalda Street at its junction with Barrack Street, Hamilton.
"I would urge any drivers or pedestrians who were in Almada Street at that time and saw him either crossing the road or saw him walking in the area to come forward as a matter of urgency, as they may have information that is vital to this enquiry."
Earlier in the afternoon of the day he was last seen, Mr McSwiggan boarded a 201 bus on Hamilton Road, Motherwell, and got off it ten minutes later at Blackswell Lane in Hamilton.
Police asked anyone with any information to contact them on 101.