Florida teen Clay Moore just wants to get back to having a normal life after being abducted for ransom by a man who may be trying to flee to Mexico, his family said Tuesday.

"We are truly proud of Clay; he did an incredible job on his own," Traci Kelle, Clay's mother, said during a press conference. "He kept his head about him. We're thankful. We're grateful he's back home with us. We believe he did the right thing."

Clay, 13, who also attended the press conference, used a safety pin he hid in his mouth to tear the tape that was over his mouth, hands and feet after his abductor left him in the woods in Manatee County, Fla.

"We're proud of Clay ... he's the one that saved himself," said Clay's father, Tim Moore. "I just want to say once again how proud we are of you."

Early Friday morning, Clay was ordered to get into a red Ford Ranger from a Parrish bus stop, bound and taken to a wooded rural area about 20 miles from where he was abducted. They believe Vicente Ignacio Beltran-Moreno planned to keep Clay tied up in the woods until a ransom was met.

The safety pin played a key role in Clay's escape. His stepfather, Stephen Kelle, said Clay had a rip in the hooded jacket that was part of his school uniform.

"Instead of buying him a new one, we told him basically to 'pin it up,' because it's kind of his fault. So he had to use a safety pin to keep his sleeve in tact," Stephen Kelle said.

While Clay was in his abductor's truck being driven from the bus stop, he took that pin from his jacket and put it into his mouth. When Stephen Kelle asked Clay Monday night why he even thought about that move, Clay said, he "just thought it would be helpful," Stephen Kelle said Tuesday.

He was left in the woods, bound, with one of his socks in his mouth, "which is truly unimaginable, even to us today," Stephen Kelle said.

A while after his abductor left the woods, it became quiet, Stephen Kelle said. Because it was a hot and sticky day, Clay was able to maneuver the tape binding him. He pushed the sock out of his mouth, the safety pin dropped to the ground, and using a stick and his mouth, he was able to pick up the safety pin and drop it into his hands. He then used it to free his hands and feet.

Clay then walked for hours to a nearby farm and used a farmer's cell phone to call his parents.

"Then I got a phone call I will never forget … I almost didn't answer it," Stephen Kelle said, because he didn't recognize the number. "I heard a voice as calm as if he was calling from a friend's house. He told me, 'Steve, it's Clay and I've been kidnapped.'"

Added Traci Kelle: "When I got his phone call, it was the best thing that ever happened in my life. I'm so proud of him. He was very smart and kept his head on him."

Manatee County Sheriff Charlie Wells indicated the safety pin plays a larger part in the investigation, but he would not elaborate.

The family asked that anyone with information about Clay's suspected abductor come forward. While they thanked law enforcement, media, volunteers and anyone else who helped in the search for Clay, the family also asked that the media allow them to get back to normal after the ordeal.

"We'd like to ask for some privacy to kind of let Clay and his little brother be little boys," Stephen Kelle said. "They just want to go outside again, play in the street with their friends, without having people come up behind him asking them all these questions."

Authorities on Sunday issued a warrant for Beltran-Moreno, 22, who authorities say is Mexican. They believe he kidnapped Clay at random as a way to collect a ransom.

"We have reason to believe he has fled the area but we're not 100 percent sure," Manatee County sheriff's spokesman Dave Bristow told FOX News Monday morning, adding that authorities are searching both locally and out of state.

Asked whether Beltran-Moreno may be trying to flee to Mexico, Bristow said: "Certainly there's a chance of that and we're working with authorities there and hopefully we'll be able to catch up with him soon."

Bristow said police are not sure if Beltran-Moreno was in the United States legally or not, since there are several men who share the same name.

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Authorities said Beltran-Moreno is a former migrant worker at the farm where Moore was ultimately found. Police believe Beltran-Moreno, most recently employed with an aluminum contractor, has fled Florida. Police want to bring him back to Manatee County to stand trial for Clay's kidnapping.

Authorities executed a search warrant on one location early Sunday morning and recovered a rough draft of a ransom note, Wells said.

Parrish is about 30 miles southeast of St. Petersburg. The bus stop where the abduction occurred was at the entrance to a subdivision off a rural road in eastern Manatee County.