Samantha Power made the remark in an interview with Scotsman political correspondent Gerri Peev.
"She is a monster, too – that is off the record – she is stooping to anything," she told the newspaper.
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Hide Ad"Here, it looks like desperation. I hope it looks like desperation there, too."
Robert Gibbs, Obama's communications director, said: "She made the decision to resign and we accepted it."
In a statement issued following publication of The Scotsman story, Ms Power said her comments "do not reflect my feelings about Senator Clinton, whose leadership and public service I have long admired" as she apologised to both Mrs Clinton and Mr Obama.
"I should not have made these comments, and I deeply regret them," she said.
"It is wrong for anyone to pursue this campaign in such negative and personal terms."
More on this story in Saturday's Scotsman