Police said a family of five from Nebraska were on holiday and wading in a lake near the Grand Floridian Resort & Spa when the attack happened on Tuesday evening. The boy’s father tried to rescue the boy.
Jeff Williamson, a spokesman for the Orange County Sheriff’s Department, said the effort was still considered a search and rescue operation.
“We are very hopeful. Sometimes you get the worst, but we are hoping for the best.”
The attack happened in an area where “no swimming” signs were posted. The alligator was estimated to be four to seven feet long, but its exact size was not known.
The beach area is part of the luxury Grand Floridian resort, across the lake from Disney’s Magic Kingdom theme park.
It was reported all resort beaches at Walt Disney World were closed following the incident.
More than 50 law enforcement personnel searched the well-tended lagoon along with an alligator tracker and two marine units in an effort that continued through the night.
Mr Williamson said more personnel were being brought in to offer some “fresh eyes” for the search.
Nick Wiley, of Florida Fish and Wildlife Conservation, said it was rare for people to be attacked by alligators, but he added that the creatures move around.
He said four alligators were taken from the water overnight, but officials found no evidence they were involved.
He said the alligators have to be euthanised before they are analysed.
Williamson said the boy was at the edge of the water, probably about a foot or two into the water, when the alligator attacked. He said Disney’s boats were the first ones in the water.
Disney spokeswoman Jacquee Wahaler said everyone at the resort was devastated by what happened and Disney is helping the family. When asked if Disney was aware of alligators on the property, Ms Wahaler advised there were signs that said “no swimming.”
Mr Williamson brushed aside’ questions about the odds of rescuing the child at this point. Right now, hopefully, we’re searching for a little boy to bring the family some comfort,” he said.
He wouldn’t speculate on how long the search would continue. “We’re just trying to find a young boy. We’re just going to keep searching until we find something. We’ll call it off when we call it off.”
There have been no other recent reports of similar alligator attacks on the lake.
In March 1997, a three-year-old boy was killed by a 450lb alligator that grabbed him and dragged him into Lake Ashby in Volusia County as he walked on the shore with his dog.
Wildlife officials shot the alligator, which was still holding the boy’s body 20 hours later.
The Nebraska governor Pete Ricketts said his heart went out to the family. The family’s name has not been released, and his office said in a statement that all they know was what they have seen in media reports.
Mr Ricketts said “no family should ever have to experience such horror”.
A total of 22 people have been killed by alligators in Florida since 1948.