The search for Ian John McLoughlin, 55, follows the death of Graham Buck, 66, in a Hertfordshire village on Saturday.
McLoughlin was on day release when Mr Buck was killed and the Ministry of Justice (MoJ) has said the programme of temporary release is "essential".
Police said 30 possible sightings of McLoughlin had been reported.
"Release on temporary licence is used to prepare prisoners for their eventual release from custody," a spokesman for the MoJ said.
"It helps to reduce the chance of reoffending by setting up appropriate employment and rehabilitation work in the community, and maintaining family contact.
"This is essential for successful resettlement."
McLoughlin had served 21 years of a minimum 25-year sentence for murder.
He was on an unsupervised day out from the Category D Spring Hill prison near Aylesbury when he fled.
Another man hurt in the suspected robbery, in which thousands of pounds were stolen, has been released from hospital and is currently in what police described as a "place of safety".
Det Ch Supt Jeff Hill said Mr Buck had received "fatal stab wounds" and police were treating the death as murder.
Police said they had found a number of "items of interest" at the crime scene but were unable yet to state whether the murder weapon was among them.
It was unclear whether McLoughlin was armed, police said.
Police said they believed McLoughlin may have left Hertfordshire and confirmed their search had extended across the UK.
They said ports, police forces and airports across the country had been "put on alert".
McLoughlin is known to be a heavy drinker and police have appealed to owners of guest houses, hoteliers and pubs to be "vigilant".
McLoughlin is described as white, about 6ft (1.8m) tall, with straight, greying, collar-length hair and of average build.
Anyone with information on his whereabouts has been urged to contact police or Crimestoppers.
The Ministry of Justice has defended the day release of prisoners amid the hunt for a killer wanted over the fatal stabbing of a "good Samaritan".