Authorities investigating the case were surprised by the family's request that volunteers stop searching for Lori Hacking based on new information from her husband.
The statement released late Saturday by the families of Mark and Lori Hacking did not say what Mark Hacking had told them.
Authorities would only say that the relative provided "additional substantive new information," said Detective Dwayne Baird. He declined to comment further.
Baird said police would renew a search at a municipal landfill. Cadaver dogs would not be available until Friday, however, when the all-night searching can begin, he said.
Mark Hacking's parents, Douglas and Janet Hacking, refused to comment Sunday, as did his lawyer.
Lori Hacking, 27, has been missing since July 19, when her husband told authorities that she failed to return from an early morning jog.
Lori Hacking's father, Eraldo Soares, said late Saturday that he was unaware of any new information about his daughter.
The organized search for Lori Hacking was called off by the families late last week, a decision they said was made out of concern for the volunteers' safety. The search was in neighborhoods, industrial areas and canyons near the park where Lori Hacking was said to have been jogging the morning she was reported missing.
Since that day, Mark Hacking's credibility has crumbled amid revelations that he lied to his wife about enrolling at medical school in North Carolina and about graduating from the University of Utah.
The day after Mark Hacking reported his wife missing, he was taken to a psychiatric ward after he was seen running around at night naked outside a motel where he'd taken a room.
Investigators focused on Mark Hacking, 28, after learning he was at a store buying a new mattress just before reporting his wife missing. Authorities were later seen removing a box spring from the couple's apartment. Investigators have refused to confirm reports that they found a mattress in a nearby trash bin.
Hacking has not been charged.