Detective Inspector Tom Fitzgerald said the three men may still be in the Arthur's Pass area, or may have continued towards the West Coast, where they were known to have connections.
"We are urgently seeking assistance from the public and want to hear from anyone in the area who may have seen these men, or anyone matching their descriptions,'' he said.
"They may still be travelling, or they may have gone to ground. Someone may have seen them in a vehicle or in and around Arthur's Pass at some stage since late last week.
"It's vital that anyone who has seen these men, or any other unusual or suspicious activity, comes forward to police urgently.''
Ivan Campbell was jailed for 14 years in 2001 for the horrific attack the year before.
He was paroled to live at the Salisbury St Foundation in June after serving 11 years of his sentence.
Police said both Ivan Campbell and Galland were high-risk offenders and while they posed no specific threat, they should not be approached.
The men were known to have connections in Christchurch as well as in Ashburton and the West Coast.
Ivan Campbell is described as a Caucasian, 177cm tall, of medium-thin build, with extensive tattoos on his face, neck, and arms.
Galland is described as Caucasian, 177cm tall, of medium build, with tattoos on his neck.
Jamie Campbell, aka Alexander Paul Jones, is a 25-year old, Caucasian, tall, of slim to medium build with dark hair and a beard. He is not believed to be related to Ivan Campbell.
