Parents of Boy Killed by Gator at Disney Resort Say 'Pain Gets Worse' Each Day

— -- The parents of the 2-year-old boy killed by an alligator at Walt Disney World in Florida say the pain of losing their son gets worse each day.

Lane Graves died June 14 at the Grand Floridian Resort & Spa near Orlando, when a gator snatched the boy into a man-made lake on the property, authorities said. His body was found the next day.

His parents, Matt and Melissa Graves, said in a statement today, "We will forever struggle to comprehend why this happened to our sweet baby, Lane."

"As each day passes, the pain gets worse, but we truly appreciate the outpouring of sympathy and warm sentiments we have received from around the world," they said.

"We will solely be focused on the future health of our family and will not be pursuing a lawsuit against Disney," they added.

The Graves said they hope to keep their son's "spirit alive" through the Lane Thomas Foundation.

"It is our hope that through the foundation, we will be able to share with others the unimaginable love Lane etched in our hearts," they said.

Walt Disney World Resort President George Kalogridis said in a statement today, "In the wake of this tragic accident, we continue to provide ongoing support for the family, which includes honoring their request for privacy."

Disney Chairman and CEO Robert A. Iger said in a statement last month, "As a parent and a grandparent, my heart goes out to the Graves family during this time of devastating loss."

"My thoughts and prayers are with them, and I know everyone at Disney joins me in offering our deepest sympathies," he said.

Three days after the deadly incident, Disney announced it would install new signage and barriers on the beaches of its Disney World resorts.

The new signs say there are "alligators and snakes in area" and warn visitors to stay away from the water and not to feed the wildlife. Previous signage warned not to swim in the water but did not mention alligators.

Disney is also "working on permanent, long-term solutions at our beaches," Walt Disney World Resort Vice President Jacquee Wahler said in a statement on June 17. "We continue to evaluate processes and procedures for our entire property, and as part of this, we are reinforcing training with our cast for reporting sightings and interactions with wildlife and are expanding our communication to guests on this topic."

Disney is the parent company of ABC News.