Washington (CNN) The campaign of Sen. Amy Klobuchar said she has "deep respect" for the family of John McCain after the late senator's daughter, Meghan McCain, asked the 2020 Democratic candidate to keep her father out of presidential politics.

"Senator Klobuchar had a long time friendship with Senator McCain, she has defended him against President Trump's attacks in the past, and she has deep respect for his family," Klobuchar's communications director, Tim Hogan, said in a statement Monday night. "While she was simply sharing a memory, she continues to believe that the best stories about Senator McCain are not about the views he had about President Trump: they're about McCain's own valor and heroism."

The back-and-forth over McCain began Saturday, when, during a campaign event, Klobuchar recalled the Arizona Republican said the names of dictators to her during President Donald Trump's inauguration speech in January 2017.

"John McCain kept reciting to me names of dictators during that speech, because he knew more than any of us what we were facing as a nation," Klobuchar told voters in Iowa. "He understood it. He knew because he knew this man more than any of us did."

Meghan McCain rebuked Klobuchar on Monday for invoking her father's memory to criticize Trump.

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