"The past week has been incredibly difficult," Kardashian wrote on her website Tuesday. "I am so thankful to family, friends and fans, who have sent nothing but prayers and well wishes to Lamar."
Kardashian, who married Odom in 2009 before separating in 2013, also thanked the staff at Sunrise Hospital in Las Vegas.
Odom, 35, was rushed to a hospital last Tuesday after he was found unconscious at a brothel in Nevada. He was in a coma for three days before regaining consciousness. On Monday, he was moved to Cedars-Sinai Medical Center in Los Angeles to continue treatment. The incident is under investigation.
"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. "Thank you for your continued support. God is great!!!"
Kardashian and Odom are not yet officially divorced. During his hospitalization, she was responsible for making decisions regarding his medical care.