Ian John McLoughlin, 55, is wanted over the death of Graham Buck, 66, in a village in Hertfordshire on Saturday.
Hertfordshire Police said Mr Buck died while intervening in a robbery at his neighbour's home.
McLoughlin had served 22 years of a minimum 25-year sentence for murder, police said.
He was serving his sentence at the Category D HMP Spring Hill, near Aylesbury.
The Ministry of Justice (MoJ) said it would not comment on individual cases but was "supporting" police with the investigation.
Det Ch Supt Jeff Hill said Mr Buck had received "fatal stab wounds" and police were treating the death as murder.
"Mr Buck's actions were totally selfless and illustrate a deep sense of community spirit which deserves recognition and respect," he said.
He added that McLoughlin "may well have left the country".
"Following the incident on Saturday the suspect caught a taxi to Watford and he was dropped off somewhere near the Horn Pub in Hempstead Road," he said.
"We also have potential reports of a sighting yesterday afternoon at around 14:30 in Bedmond, Hertfordshire."
McLoughlin is described as white, about 6ft (1.8m) tall, with straight, greying, collar-length hair and of average build.
He is believed to have been wearing sunglasses, blue jeans or three-quarter length trousers and a dark blue, light blue and white checked short-sleeved shirt with a button-down collar.
Mr Buck was born in London and lived in Surrey and Sussex before moving to Hertfordshire in 1995.
Since his retirement he had worked as a non-executive director at Aldwyck Housing Association in Houghton Regin, Bedfordshire.
His wife, Karen, said she had lost her "rock".
"I don't know what I'll do without him," she said.
Mr Buck, who was described by his family as a "truly genuine person" had two sons, a daughter and two grandchildren.
It is understood the apparent intended victim and McLoughlin know each other from prison.
The man was treated in hospital for injuries sustained during Saturday's attack but has since been released.
Anyone with information has been urged to contact police or Crimestoppers.
A "dangerous" man being sought by police investigating the death of a man stabbed while protecting a neighbour, was a murderer on day release.