Thompson insisted he has the "utmost respect and love" for Khloe, and said he is "incredibly sorry".
He added: "My actions certainly have not lined up with the way I view you. I have the utmost respect and love for you. Regardless of what you may think. Again, I am so incredibly sorry."
Thompson's paternity test results come after Nichols filed a lawsuit against him for child support, claiming he was her son's father, following the birth on December 1.
But she said: "I did not file any request for child support before our child was born."
Thompson also has a son Prince, 5, with his ex Jordan Craig.
Just last week, Kardashian admitted she wants to grow "stronger" and smarter" by learning from "painful moments" in her life.
She shared two cryptic posts on her Instagram Story as she reflected on 2021 and how she can tackle the year ahead.
The first post read: "People showed you who they were this year. Don't go into 2022 confused."
The second read: "There's going to be painful moments in your life that will change your entire world in a matter of minutes. These moments will change YOU.
"Let them make you stronger smarter and kinder. But don't you go become someone that you're not.
"Cry. Scream if you have to. Then you straighten out that crown and keep it moving."