Following her interview with Oprah Winfrey on Monday, former vice presidential candidate Sarah Palin continues to promote her book, sitting down with Barbara Walters to set the record straight about claims made by Levi Johnston that her marriage is on the rocks and that she called her youngest child Trig a derogatory term.

Johnston, 19, claimed on "The Early Show" last month that Palin had called Trig, who is afflicted with Down syndrome, "retarded."

"That's heartbreaking to know that that he would say such a thing and that's not true," she tells Walters, who aired her interview with Palin on "Good Morning America."

Johnston -- the father to Palin's grandchild Tripp -- has also told media outlets that he thinks the former Alaska governor and her husband Todd will divorce. Palin reacts, "We remain a solid, blessed couple."

Walters addresses Johnston's claims that Palin did not mention him in her book Going Rogue: The American Life because she feared what information he had on her. "He doesn't have anything on me," Palin says of Johnston's remarks.

The former VP hopeful believes it's a "good sign" that Johnston has said he is going to court to get joint custody of his son Tripp. "It will be nice to see a desire to be a part of the baby's life."

See Johnston's reaction to Palin's Oprah interview...

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