Carlee Russell's parents insist there was an abductor following her mysterious 48-hour disappearance

The parents of an Alabama nursing student who returned home safe 48-hours after she mysteriously disappeared have spoken out to insist an 'abductor' was behind her disappearance.

'Carlee has given detectives her statement so that they can continue to pursue her abductor,' said Carlee Russell's mother Talitha Russell in an interview with the Today Show on Tuesday.

Pressed on whether they believe an abductor is at large in the case, Talitha responded 'absolutely, absolutely,' as Carlee's father Carlos nodded in agreement.

Questions about the case have swirled since Carlee Russell reappeared at her parents' home in Hoover on Saturday night, 48 hours after she disappeared from the side of an interstate after calling 911 to report seeing a toddler on the roadside.

Hoover Police Department Captain Keith Czeskelba told DailyMail.com in an update on Tuesday morning: 'We have spoken to Carlee once and are following up on that information, however we are not able to publicly share the details from our initial interview.' 

'We will follow up with her again to attempt to get a better understanding of her movements during the time she was missing and will provide what information we can when we are able to do so,' he added.

'Carlee has given detectives her statement so that they can continue to pursue her abductor,' said Carlee Russell's mother Talitha Russell in an interview on Tuesday

Carlee Russell, seen with her boyfriend above, reappeared at her parents' home in Hoover on Saturday night, 48 hours after she disappeared from the side of an interstate

Police have remained tight-lipped on whether they are seeking a suspect in the case, and the strange circumstances of Carlee's disappearance have so far left more questions than answers.

In the new interview, Carlee's parents said they they were subjected to cruel taunting and fake messages claiming to have information about their daughter while she was missing.

'There were actually just so many calls and texts from people who maliciously lied to us,' Talitha Russell said. 'I just didn't know people could be so evil.' 

The mother grew emotional as she described the moment she was reunited with her daughter, saying the reunion was filled with 'so much joy'. 

'We tried to hug as best we could, but I had to stand back because she was not in a good state. So we had to stand back and let medical professionals work with her,' said Talitha.

Police have not yet released information about what happened to Carlee or where she was during their two-day search.

The nursing student, 25, called 911 at 9.34pm on Thursday night and reported that she was stopping along an interstate to check on a toddler she saw there, police said. 

Russell's 911 call was the only timely report of a child on the interstate, police said Monday. 

After the 911 call, her family said she was on the phone with her brother's girlfriend, who didn't hear a child but did hear Carlee Russell scream. The line remained open but Carlee stopped responding.

Within five minutes of being dispatched, Hoover police officers arrived and found Russell's wig, cellphone and purse with her Apple Watch inside on the road near her vehicle. 

At 10.44pm on Saturday, a 911 caller reported that Russell has returned home to her parents' house on foot. 

Russell was taken to a hospital to be evaluated, and she was treated and released. Detectives went to Russell's home and the hospital to take a statement from her. 

Developing story, more to follow.