Kim responded after host Ryan Seacrest asked if she's rooting for Khloe and Thompson in spite of the scandal. She chose her words carefully, suggesting Thompson blocked her on social media after a previous interview.
"Last time I went on TV and answered some questions about her, I got blocked on social media," the star said, referencing her recent interview with The Ellen DeGeneres Show. "Not from Khloe."
"I'm always rooting for her. I'm always rooting for love," she answered. "I'm always rooting for families."
Kim had called Khloe's situation with Thompson "messed up" on the April 30 episode of Ellen.
"We really were rooting for Khloe and we still are," the television personality said. "She's so strong and she's doing the best she can."
"I kind of made this rule ... if there's a baby involved, I'm going to keep it cute, keep it classy and try not to say anything negative," she added.
Khloe gave birth to daughter True Thompson in April. She gave fans a first glimpse of the infant in a Snapchat photo Thursday following her first postpartum workout.