The parents of a Nebraska toddler killed by an alligator at Florida's Walt Disney World said Saturday they are overwhelmed by the support they have received since the death of their son.

Matt and Melissa Graves of Omaha, Nebraska, said in a statement they appreciate the support and love from friends in their community and around the country.

"Melissa and I continue to deal with the loss of our beloved boy, Lane, and are overwhelmed with the support and love we have received from family and friends in our community as well as from around the country," the family said. "We understand the public's interest, but as we move forward this weekend, we ask for and appreciate the privacy we need to lay our son to rest. Neither Melissa, myself or anyone from our family will be speaking publicly; we simply cannot at this time."

Sara Brady, who is serving as a spokeswoman for the family, declined to comment on when the funeral has been scheduled.

An alligator described as being as long as seven feet snatched two-year-old Lane Graves as he waded in shallow water in a lake at a Disney hotel Tuesday night. The boy's remains were found after a long search the following day.

An autopsy showed that he died from drowning and traumatic injuries, according to the Orlando medical examiner.

The beach, located at Disney's Grand Floridian Resort and Spa across a lake from the Magic Kingdom, had "no swimming" signs but no warning about alligators.

The company added alligator warning signs on Friday. The resort's beaches remain closed.

Construction workers have started to put up wooden posts connected with rope along the edge of the lagoon where Graves was snatched.