The 31-year-old reality TV star thanked family, friends and fans for support as well as hospital staff who have cared for Odom since he was found unconscious at a Nevada brothel on Oct. 13. Reports said alcohol, cocaine and sexual stimulants were found in Odom's system.
Kardashian, whose divorce from Odom is pending but not final, has stayed by Odom's side since his hospitalization. People reports that her current boyfriend, Houston Rockets shooting guard James Harden, has been supportive.
Odom, who was in a coma for four days, spent a week at Las Vegas Sunrise Hospital & Medical Center before being airlifted to Cedars-Sinai Medical Center in Los Angeles Monday.
"The past week has been incredibly difficult. I am so thankful to family, friends and fans who have sent nothing but prayers and well wishes to Lamar. I also want to take a moment to thank everyone at Sunrise Hospital, inlcuding the amazing doctors and nurses for their kindness and diligent work. Under their amazing care, incredible, strides have been made. You can never be prepared for an experience like this, but without the outpouring of love and endless prayers Lamar has received and the strength I was given from my loved ones, it would have been difficult to endure. Thank you for your continued support. God is great!!!"
Her family has also posted encouraging messages on social media.