LAKE BUENA VISTA, Fla. - The body of a 2-year-old boy who was dragged underwater by an alligator at an upscale resort at Disney World in Florida has been found, the local sheriff said Wednesday afternoon.

The boy's family from Nebraska was on the beach of the Seven Seas Lagoon at about 9:20 p.m. Tuesday when he was snatched and the father tried to fight the alligator but failed to free him.

By Wednesday morning, with no sightings of the boy, Orange County Sheriff Jerry Demings said, "There's no question" the boy had perished.

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Demings said that at about 3:30 p.m. Wednesday the remains were recovered by divers not far from where he was last seen.

The child has been identified as Lane Graves from Elkhorn, Nebraska, and his parents are Matt and Melissa Graves.

Neighbors told CBS affiliate KMTV in Omaha that the family went on vacation last Thursday, having stopped in Georgia before heading to Disney World.

KMTV has learned the couple has two children, the two-year-boy and a four-year-old daughter, who was in a playpen at the time of the attack.

Demings said he delivered the news to the family with a Catholic priest.

"Of course the family was distraught, but also I believe somewhat relieved that his body was found intact," Demings told a news conference.

Demings said the body was completely intact. Although an autopsy is yet to be performed, Demings said he believes the boy drowned.

The boy's father, Matthew Graves, suffered lacerations to his hand trying to save his son from the gator.

Lane Graves. Orange County Sheriff's Office

Graves is chief data officer for Infogroup, a marketing company based in Papillion, Nebraska, whose chairman Michael Iaccarino says he's "stunned and heartbroken" over the "family's unspeakable loss."

He says, "Matt's family is the light of his life, and his family's anguish is our own."

The search -- which covered a large, man-made lake and included boats, helicopters and divers - has been suspended. At least five alligators were captured and cut open in the hunt for the boy.

Many questions have arisen about the safety of the beach for visitors who might not be aware of the state's large alligator population. Demings said there was signage in the area of the attack advising no swimming.

The boy was said to be wading in ankle-deep water when the attack took place.

"Disney has a wildlife management in place and they have worked diligently to ensure their guests haven't been exposed," Demings said, adding that in the 45-year history of the resort, this is the first such attack.

Nick Wiley, executive director of the Florida Fish & Wildlife Conservation Commission (FWC), told CBS News that if a gator "attacks a human it's mistaken."

Wiley said he had nothing but praise for the resort for being "very proactive in dealing with alligators."

The wildlife director said that officials will keep scouring the lagoon for other alligators in the hopes of identifying the one that took the boy.

The president of the Walt Disney World Resort issued a statement.

George A. Kalogridis says "there are no words to convey the profound sorrow we feel for the family and their unimaginable loss.

"We are devastated and heartbroken by this tragic accident and are doing what we can to help the family during this difficult time. On behalf of everyone at Disney, we offer our deepest sympathies."

In the past, when Disney officials have discovered alligators in the large lagoons near their resort they have largely been removed and euthanized.

Disney has closed its beaches at all of its properties in Florida as they assess the incident.

Since 1973, 23 people have been killed by wild alligators in Florida, according to data compiled by the Florida Fish and Wildlife Conservation Commission. Those fatalities were among 383 unprovoked bites not caused by someone handling or intentionally harassing an alligator.