Investigators on the hunt for a missing 5-year-old girl in Utah believe Elizabeth "Lizzy" Shelley is hurt, although they do not know her exact condition, police revealed Tuesday.

"We would never dash the hope that we would find her alive," Logan Police Chief Gary Jensen said at a news conference. "But, it's certainly a concern for us at this point, Lizzy's safety."

Police reiterated that the girl's 21-year-old uncle, who they said has been “uncooperative,” is the suspect in her disappearance.

Jensen said investigators have "strong evidence" including DNA linking the uncle, Alex Whipple to her disappearance. She initially was reported missing Saturday morning.

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Police said they were called around 10 a.m. Saturday for a report of a missing 5-year-old. They said Whipple showed up to the home on Friday evening, according to family, and they were all in the house at 2 a.m. Police said when the family woke up the next morning around 9 a.m. they said they couldn’t find Shelley -- and Whipple was no longer in the home. They searched for a while before calling police.

Officers found “several items of interest a short distance from the home,” police added. They said the items were tested and showed “forensic evidence of 5-year-old Elizabeth Shelley.”

Whipple was found in a rural area around 10 miles from the family home and was arrested Saturday afternoon. Police said he was combative and “failed to identify himself and had a warrant for his arrest for not checking in with probation for his recent charges of receiving stolen property and driving under the influence.” Police added that he also was in possession of drug paraphernalia.

He was in custody on a probation violation and has not been charged in Shelley’s disappearance.

Whipple was denied bail Tuesday during a court hearing in Logan in which he appeared via video.

His attorney, Shannon Demler, had argued that Whipple should get bail because he has not been charged in connection with the disappearance.

Logan City Police said when Whipple was interviewed by detectives he “made several inconsistent statements at the very beginning and lied about his whereabouts which were already known.”

Police said Whipple was “uncooperative throughout the interrogation.”

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Several search warrants were obtained and executed Sunday night “on several crime scenes and for evidence from Alex Whipple’s person,” Logan City Police wrote on the department’s Facebook page. “The evidence obtained from Alex Whipple was tested and there are confirmed forensic evidence from Elizabeth Shelley located from off his person.”

Whipple has a criminal record that includes an assault involving domestic violence, possession of a stolen vehicle and drug-related charges.

Logan City Police said multiple agencies including more than 200 local, state and federal police officers, as well as dozens of Search and Rescue personnel, were continuing to work day and night to try finding Shelley.

The ongoing search has been concentrated on a one-half mile area around the family's home in Logan, in a picturesque mountain valley near the Idaho border about 80 miles north of Salt Lake City.

Police have continued to ask the public if they saw Whipple or Shelley on Saturday to contact them. The also asked people in the area to check their yards, buildings and garbage cans for anything they didn’t recognize.

The Logan City Police Department thanked the community for their continued support. They posted pictures of all the supplies donated by people and businesses in the area on the department’s Facebook page.

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“All these contributions provide our searchers and investigators nourishment and more importantly heartfelt support in their efforts to solve this case,” Logan City Police wrote in the Facebook post.

“Logan City Police Department sincerely extends a huge thank you to this wonderful community for their enormous support."

Fox News' Faith Mangan and The Associated Press contributed to this report.