Douglas Bruce, 78, was reported missing from Peterculter on the outskirts of Aberdeen at around 9.15am that day.
Searchers, including coastguards and a police diving team, have been focusing their efforts on the banks of the River Dee and wooded areas nearby.
After a third day of looking today, police said they are "increasingly anxious" to find the missing man.
Detective Sergeant Gary Winter, of Police Scotland, said: "Searches have continued today around Mr Bruce's home address, the route he was seen to have walked after leaving his home, and an area by the River Dee.
"A walking stick believed to have been Mr Bruce's has been found near to the River Dee."
Officers have appealed again to the public to contact them with any information about his disappearance.
"I would continue to urge members of the public to check their outbuildings and sheds and to come forward if they may have information," said Mr Winter.
"I would also ask anyone who frequents the River Dee area to come forward if they think they may have seen Mr Bruce.
"We are reviewing CCTV in the area and enquiries are ongoing. We are growing increasingly anxious to trace Mr Bruce."
Mr Bruce is 5ft 2in and of medium build with grey-white hair. He usually wears glasses with silver rims.
When he was last seen he was wearing a black or navy jacket with a hood, grey trousers, brown boots, a dark beanie-style hat and a dark scarf.