The last confirmed sighting of 73-year-old Ian Collinson was at about 12.30pm on Tuesday.
He was spotted on the bridge over the A1 near Hartley Wood, Micklefield, which is a short distance from his home.
Detective Inspector Steve Greenbank, of Leeds District CID, said: “We remain very concerned for Ian’s welfare given his age and health, but particularly given the amount of time that he has now been missing.
“We have been conducting extensive enquiries to trace him along with physical searches on the ground, and that work will be continuing.
“The focus of the searches has been based around the last confirmed sighting that we have of him but we are also following up other potential sightings.”
Officers have carried out a number of searches of the area under the direction of police search specialists and with support from volunteers from Calder Valley Search and Rescue Team.
The Yorkshire and the Humber Underwater Search and Marine Unit has been searching nearby Sheep Dike, while checks have also been made with hospitals and transport providers.
Det Insp Greenbank said: “Ian is clearly well known and well liked in the community and we are grateful to everyone who has rung in with information.
We are also grateful to everyone who has offered to help with searches, although at this stage we don’t require the public’s assistance with those.
“People can help us best is by getting in touch with any sightings of Ian or any information that could assist us in establishing his whereabouts.”
Mr Collinson, 73, is described as white, about 5ft 7in and slim, with short, white hair. He wears glasses and uses a walking stick and was wearing blue jeans.
Anyone with information is asked to contact the Special Operations Room at Elland Road via 101 quoting log number 1908 of August 23.