The reality TV star wrote that it has been an "incredibly difficult" week, and that she is grateful for all of the prayers and support she has received from family, friends and fans.
"You can never be prepared for an experience like this, but without the outpouring of love and endless prayers that Lamar has received and the strength I was given from my loved ones, it would have been difficult to endure," Kardashian wrote.
Odom was fighting for his life after being found unconscious at Love Ranch in Crystal, Nev., last Tuesday. Late last week, the former NBA champion regained consciousness, and according to his family, he has been making great progress in his recovery.
Kardashian previously released a brief statement last week on her app, notifying fans that she, along with her sisters, would be taking a break from posting content on their apps while they continued to "support and pray for Lamar."
In her new statement, Kardashian thanked the staff at the Las Vegas hospital where Lamar was being taken care of this past week.
"I also want to take a moment to thank everyone at Sunrise Hospital, including the amazing doctors and nurses for their kindness and diligent work," Kardashian wrote. "Under their amazing care, incredible strides have been made."
Odom was recently discharged from Sunrise Hospital, and transported to an undisclosed hospital in Los Angeles to continue his recovery.