Odom has two children with ex-girlfriend Liza Morales -- 17-year-old Destiny and 13-year-old Lamar Odom Jr. The three, along with Odom's aunt JaNean, flew out of New York City on Wednesday to be by the basketball pro's side at Sunrise Hospital in Las Vegas.
The kids broke their silence for the first time on Thursday. "Thanks for your outpouring of prayers and support for our dad," Destiny and Lamar Odom Jr. said in the statement to ET. "We are here with our family and friends. We appreciate everyone respecting our privacy at this time. We ask for your continued prayers."
His estranged wife, Khloe Kardashian, has remained by his side since Tuesday night, with many of her family members -- including her mom, Kris Jenner, and sisters, Kim Kardashian, Kourtney Kardashian and Kylie Jenner -- joining her at the hospital, though they have since left Vegas.
After suffering a heart attack and organ failure, Odom was placed in a medically induced coma and on dialysis on Wednesday. He opened his eyes after about 72 hours in the coma, and ET was previously told he was in critical condition.
ET will update with more information as it comes in.