The 60-year-old actress and television personality praised Osbourne, 67, during Tuesday's at-home episode of Watch What Happens Live following a heated discussion on The Talk.
Osmond and Osbourne clashed on The Talk in April while discussing coronavirus (COVID-19). Osmond said on WWHL that the disagreement hasn't affected their friendship.
"Don't believe anything you read -- Sharon and I are great friends," she said. "Everybody who sits at that table is a very strong woman, and so she'll say things and I'll go, 'Uh, no.' That doesn't mean you don't like each other."
Osmond said she doesn't think Osbourne owes her an apology.
"No. She doesn't owe me anything," she said.
Osmond again praised Osbourne as a "strong" woman.
"We're very different, and yet we're very similar in ways. We're both strong women," she said. "I mean, I've been in this business, this is my sixth decade, and so, you know, I've been around."
Osbourne spoke out April 2 on Instagram after some fans said she owed Osmond an apology.
"For all the viewers that thought I was rude to Marie today. I would just like to say that we're all grown women and we have different opinions. It certainly doesn't mean that we don't love and respect each other," Osbourne wrote.
"As you know, these are very difficult times and they're going to bring out different emotions in all of us. I'm sorry but I can't apologise for being overly emotional, otherwise I'm being fake and I don't do that very well," she said. "Stay in, stay safe and hope to see you tomorrow."