A major investigation is under way following the three deaths in Tidworth, Wiltshire.
Officers say that although they are not looking for anyone else in connection with the incident, they are treating it as suspicious.
Since the alarm was raised on Saturday afternoon, police have been trying to piece together the last movements of the man and the two children, who are believed to be his young sons.
Detective Chief Inspector Ian Saunders, who is leading the investigation, described the case as "very tragic".
He said last night: "Yesterday afternoon the flat was due to be examined by a landlord who was showing prospective tenants around.
"The flat was set to become vacated, and as the landlady came to the property that is when she saw what she did.
"Police were then called and discovered the bodies of a 36-year-old man and two male children – aged 11 and 3. At this stage we have not yet formally identified the deceased.
"But I can say that we are not looking at any third party involvement."
Following the discovery at Auchinleck House, Sidbury Heights, police closed off the scene and conducted door-to-door inquiries.
DCI Saunders said initial information revealed that the last-known activity in the flat was last Thursday morning.
"As the investigation progresses, we will begin to find out exactly what happened in this very tragic case," he added.
One key piece in the jigsaw is the results of the post-mortem examinations. Morticians in Bristol will examine the man, while their colleagues in Southampton will carry out tests on the children.
A specialist team of officers has also been assigned to support family members.
Among them is the boys' mother – who is said to have separated from their father. "It has clearly been a shock for her to find out and she is very distressed," said DCI Saunders. "But she will be given the best possible support we can provide."
News of the tragedy has sent shockwaves through the town and particularly its Sidbury Heights estate – which is home to many families.
Neighbours have continued to leave flowers, toys and messages of condolence outside the building's main entrance.