McCullen told police he put Jordan down for a nap around 1 p.m. Monday and left her to take a nap himself. He told authorities that she was gone and the front door open when he awakened around 3:30 p.m.
Authorities did not elaborate on a motive behind the killing.
The remains found Tuesday were partially concealed, according to the Gaston County District Attorney's Office. They were discovered in a wooded area near Jordan's home.
Ramey would not give information about the condition of the remains, how long they might have been there or if there were any visible wounds or injuries.
"We appreciate everyone's assistance," Ramey said, "(but) we do not believe we have gotten the outcome that we were hoping for."
The FBI is helping to investigate the case.
Gaston County emergency officials and about 100 volunteers searched earlier Tuesday for signs of Jordan near Bessemer City.
Many volunteers -- some of whom started their search at 7 a.m. -- were in tears when they learned that a body had been discovered. The group was made up mostly of strangers, although some were neighbors of Jordan's family in Bessemer City.
A ground search was launched after Jordan was reported missing Monday afternoon. It was suspended around 9:30 p.m., although a helicopter equipped with a heat-sensing camera continued the search overnight. Neighbors continued to comb through the woods overnight as well.
"We've been working through the night," Ramey said. "We've been out here all night. In addition, we've been following up additional leads that weren't on this scene."