The mission was still considered a search and rescue operation even though the toddler had been missing since late yesterday, Orange County Sheriff Jerry Demings said at a sunrise news conference.
"We determined this two-year-old child was playing at the edge of the water, a foot or so into the water, when this alligator came up and attacked the child," he said.
"The father did his best. Tried to rescue the child, however, to no avail."
The lake is part of a Disney complex that includes another hotel. Both are connected to the Magic Kingdom, one of four theme parks at the Walt Disney World Resort in Orlando.
"We have not been able to locate that child," Demings said. "We will continue the search throughout the course of the evening."
"Multiple deputies" were at the site overnight, he added.
"More are coming this morning, fresh eyes to give another fresh look at the water. We'll have deputies in the air as well."
"We are very hopeful, hoping for the best," Demings said. "Sometimes you get the worst, but we're certainly hoping for the best."
Alligators are common in Florida, where they can be found in bodies of fresh water across the state, Nick Wily from the Florida Fish and Wildlife Service told reporters.
However, it is "very rare" for an alligator to attack a human, he said.
There was a no swimming sign at the lake, but no warning about alligators, Wily added.
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