Haleigh's father Ronald Cummings also said he didn't believe she had left their home in the middle of the night.
"I know somebody took her. I know for a fact she didn't wander off - she's afraid of the dark," Cummings told NBC's "Today" on Thursday.
Haleigh's mother, Crystal Sheffield, also believes someone took her daughter.
"I just want my baby here. I just want them to bring back my baby," she said, tears running down her cheeks.
Haleigh was last seen Monday night in her father's mobile home in a heavily wooded area north of Satsuma, a community along the St. Johns River about 70 miles north of Orlando. The doublewide mobile home with a screened-in front porch was blocked off with police tape Thursday.
Nearby, a team of about 30 police officers and sheriff's deputies walked shoulder-to-shoulder through the thick underbrush and palmettos. Each carried a machete to clear the brush. At times, they would stop and use a shovel to check when they found fresh dirt.
Haleigh was reported missing when her father returned home from work early Tuesday. His girlfriend told a local newspaper she had been sleeping next to Haleigh when she woke up and discovered the child was gone.
The girlfriend, 17-year-old Misty Croslin, told a 911 dispatcher that a back door that was usually locked had been propped open by a brick.
Sheriff Jeff Hardy told NBC's "Today" that searches by air, ground and water would continue Thursday. Investigators also were interviewing the 44 sex offenders living within 5 miles of Ronald Cummings' home.
John Harrell, spokesman for the northeast region of the Florida Department of Children and Families, said Thursday that his agency "was involved with the family." Harrell would not offer any details, citing state confidentiality laws.
Sheffield's family gathered at the mobile home community where the child disappeared.
Her grandmother, Nancy Griffis, 43, described Haliegh as a "highly intelligent" child who loved to play with makeup, purses, cell phones and "girlie stuff."
An uncle, Andrew Sheffield, believes she is alive, but the mystery of her whereabouts continues.
"It's fishy," he said. "Somebody knows something."
George Anthony, the grandfather of slain Florida toddler Caylee Anthony, met with Haleigh's father Thursday. Anthony said he was there simply to offer moral support.
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AP Writer Tamara Lush in Miami contributed to this report.
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