Story highlights

NEW: Tucson Police Chief Roberto Villasenor describes the agreement as voluntary

NEW: He warns against reading "too much into this"

Isabel Mercedes Celis was reported missing from her family's home April 21

Authorities have said her disappearance is suspicious, but have not identified any suspects

CNN  — 

The father of missing 6-year-old Isabel Mercedes Celis must stay away from his two sons, police in Tucson, Arizona said Monday.

“There is no legal separation at this point. This is an agreement between Sergio (Celis) and Child Protective Services that he will maintain a distance. As far as what caused that? I’m not going to comment on that at this point,” Tucson Police Chief Roberto Villasenor told reporters.

Sergio Celis is Isabel’s father. The ages of his two sons was not given by police.

During an afternoon news conference called to discuss what he described as the voluntary agreement, Villasenor warned against reading “too much into this,” and said the news does not mean that police have “settled on a path with this investigation.”

“We’re not closing the door on any possibilities,” he said.

The police chief referred questions about the separation to Child Protective Services. A call to the Arizona agency was not immediately returned.

Police have so far received more than 1,000 tips regarding the disappearance of Isabel, who was reported missing from her family’s home April 21. She was last seen by family members at 11 p.m. the night before, and a screen was found removed from one of the home’s windows, according to police.

Authorities have described the child’s disappearance as suspicious, but have not identified any suspects in Isabel’s case or indicated what they believe could have happened to her.

“Sometimes these cases depend on one big break. We’re looking for that break,” said Villasenor. “I’m not going to give up hope.”

Police have methodically searched around the family’s home and a local landfill. Authorities in Mexico have also assisted in the search.

Investigators are still pursuing tips, but the number of officers committed to the case has been pared back.

After police said they had scaled back the search, Isabel’s parents pleaded for her safe return.

“Please, please – to the person or persons who have Isa, tell us your demands,” said her father. “Tell us what you want. We will do anything for her.”

Addressing his daughter directly, he said, “We miss you so much, and we will never give up. We will never give up looking for you.”

CNN’s Shawn Nottingham contributed to this report.