Katie Couric to Kim Kardashian -- I'm Sawwwy ... I Don't Hate Your Family

Katie Couric insists her baby gift to Kim Kardashian and Kanye West was not a fake Hollywood gesture -- and says her comments about Kim's family were taken out of context.

Kim put Katie on blast today when she Instagrammed a pic of Katie's gift and card with the hashtag #IHateFakeMediaFriends.

Kim was pissed because Katie recently said in an interview that she didn't understand why the Kardashians are famous.

Now Katie's explaining the comment, saying ... "I've met Kim before and I think she's a really sweet person. I was responding to a reporter's question, and explaining how I'm intrigued by the public's fascination with her family."

She added, "I didn’t mean to hurt her feelings."

As for the gift, Katie says ... "The gift is genuine, and I'm happy for Kim and Kanye."