74 year old Paul Johnson was last seen on Wednesday night at his home in Hay Fleming Avenue.
Enquiries have since established that he was then seen at around 10.45pm on Wednesday on Hepburn Gardens in the area of Lawhead Road East in St Andrews.
He has not been seen this time and police searches have continued in the area since he was reported missing.
Inspector Murray Gibson said: “It is completely out of character for Paul to be out of contact with family for as long as this and we are growing increasingly concerned about his wellbeing as time passes.
“It is believed he left home to go for a walk but has not returned home.
“I would urge anyone who believes they may have seen Paul at any time since 10pm on Wednesday to get in touch as a matter of urgency.
“Anyone who believes they may have seen Paul or who has any information which could help trace him is asked to call 101, quoting incident 0266 of 16 September.”
Paul is described as being around 5ft 9in tall and of slim build with grey hair.
He was last known to be wearing a blue rain jacket and light coloured walking trousers.