New York (CNN) -- The man who rescued an 11-year-old girl lost in a dense Florida swamp said Wednesday that God led him directly to her and that finding her was no surprise.

James King said he set out on his own to look for Nadia Bloom on Tuesday, trusting that he was going in the right direction even when that meant through water or dense brush.

"I was expecting to hear her voice," King told CNN. "So I'm yelling, 'Nadia!' and at one point, I yell, 'Nadia!' and I hear 'What?' And I said that way -- right there."

Tanya Bloom, Nadia's mother, said later Wednesday that the family is "so fortunate God used him to bring her back."

"She's doing remarkably well," Bloom said. "She has swollen feet and lots of bug bites and scratches, but she's doing great."

Dr. Mary Farrell, who treated the girl when she arrived at the hospital, said that Nadia was in good shape but that she would remain hospitalized a little longer because of a bacterial infection.

"When she got here, she was a little bit dehydrated but she had been resuscitated pretty well," Farrell said, "and she looked remarkably well considering she had been out for four and half days."

King said he was surprised at the good shape Nadia was in. She had been missing since Friday. Shoeless and covered in insect bites, she was in otherwise good condition, he said.

"She was not panicked. She looked like she had been sitting there, waiting on me," he said.

The two of them then stayed in the swamp, near Lake Jesup in central Florida, while King called authorities. When he got hold of the 911 dispatcher, he put Nadia on the phone.

"Hi. This is Nadia. I'm the girl who got lost," came the little girl's voice.

King said it took him "two hours of rough time" trekking through the swamp to find Nadia. He said he figures it took Nadia just as long to reach the same spot.

She told King that she had gone on a nature walk and simply got lost.

"We are so, so grateful," Nadia's father, Jeff Bloom, said. "I can't even express how we felt when she was found -- beyond words."

The swamp was so dense, King said, that the rescuers who carried Nadia out on a black cloth stretcher Tuesday had to use machetes to cut through the brush, bushes and trees.

"I see it as an answer to a lot of people's prayers," King told CNN. "I'm just very thankful, I'm thankful that God used me as a part of it to be able to find her. It's definitely a miracle.

"I didn't know where she was. The only person who knew where she was was God, and I asked him and he led me directly to her, straight -- well, as straight as you can go through the swamp."

King said he prayed the whole time he was searching, even when it seemed like he was going in the wrong direction. In one case, he said, there was water all around and he didn't know where to go.

"He said, 'Go that way.' And I'm looking at water. I said, 'Lord, are you sure?' He said. 'I got ya.' And as soon as I start walking, the ground under the water is solid. It's only about a foot and a half deep. He took care of me all the way there."

The disappearance of Nadia, described as mildly autistic, had sparked an Amber Alert that was canceled when King found her.

Both King and Nadia's family at one time attended the same church, Metro Church in Winter Springs, Florida, but they didn't know one another -- though King said Nadia did seem to register him as a friendly face when she was found.

The church held an open-air thanksgiving service to celebrate Nadia's return Tuesday evening.

"Give the glory to God," Nadia's father told reporters after seeing his daughter Tuesday.

King had brought trail mix and drinks to give to Nadia if he found her, but he also brought another important item -- toilet paper.

The swamp vegetation was so thick that the helicopter that came to retrieve Nadia and King couldn't see them on the ground. King said he heard the chopper overhead and tried to give the dispatcher directions for the pilot, but it still didn't work.

"I had brought toilet paper for signaling, and so I covered the top of a couple of bushes that were in more of an open area than I was in," King told CNN. "They still had a hard time finding me, but I used that on the top (of the bushes) and they finally were able to locate it."

Authorities questioned King after they got to safety, something King said was unexpected but understandable, especially given his ability to find Nadia so quickly.

"They also have a job to do," he said. "They have a responsibility to the community to make sure there is no foul play. And so I understand that, I understood it completely."

Coming out of the swamp was a blur with lots of hugs and praise, King said.

He said he hopes to be able to see the Bloom family again, and that Nadia even hinted he'd be welcome: "She said she might invite me to her pizza party."

