Update - 1.15pm: A search is under way for a two-year-old boy who was dragged into the water by an alligator near Disney's Grand Floridian Resort and Spa, authorities said.
The effort was still considered a "search and rescue operation", said Jeff Williamson, a spokesman for the Orange County Sheriff's Department.
"We are very hopeful," he said at a morning news conference. "Sometimes you get the worst, but we are hoping for the best."
The family of five from Nebraska was on holiday and wading in the Seven Seas Lagoon on Tuesday evening when the attack happened in an area where "no swimming" signs were posted, Orange County Sheriff Jerry Demings told a news conference earlier in the morning. The father tried to rescue his son but was unsuccessful, Mr Demings said.
The alligator was estimated to be 4ft to 7ft long, but its exact size was not known, Mr Demings said. The father suffered cuts and lacerations.
The beach area is part of the luxury Grand Floridian resort, across the lake from Disney's Magic Kingdom theme park.
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 would be brought in on Wednesday to offer some "fresh eyes" for the search.
Nick Wiley, from the Florida Fish and Wildlife Conservation, said it is 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.
Mr Williamson said the boy was at the edge of the water, probably about a foot or two into the water, when the alligator attacked. The water was dark on Tuesday night as searchers looked for the boy, Mr Williamson said. They also used a sonar boat.
Mr Williamson 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 reporters' 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.
Mr Demings said there had been no other recent reports of similar alligator attacks on the lake.
Earlier: Authorities in Orlando are searching for a two-year-old boy who was dragged into the water by an alligator near Disney's Grand Floridian Resort & Spa.
Orange County Sheriff Jerry Demings says a family of five from Nebraska was on vacation and wading in a lake when the attack happened.
He said the father tried to rescue the boy.
Mr Demings said more than 50 law enforcement personnel are searching the Seven Seas Lagoon for the boy and will keep looking.
He added there have been no other recent reports of similar alligator attacks at the lake.
Orange County Sheriff's Office spokeswoman Rose Silva said the two-year-old child was dragged into the Seven Seas Lagoon near the Grand Floridian Resort & Spa in Orlando.
It happened around 9.30pm (2.30am Irish Time) last night.