Former New York Gov. George Pataki (R) on Thursday cast doubt on Donald TrumpDonald TrumpCheney challenger wins Wyoming Republican activists' straw poll We must do more to protect American Jews 6 in 10 say they would back someone other than Biden in 2024: Fox News poll MORE's rise in the presidential polls and said that the next president shouldn't be someone who hasn't held public office.

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"I don't think anyone who hasn't held public office, and I don’t think anyone who has diminished an entire ethnic group in this country, as he did with Mexicans, should be president," he said on MSNBC's "Morning Joe" when asked about Trump's qualifications.

When pushed to clarify if that declaration applied to the entire field, Pataki walked the comments back slightly and pegged the chances of a president with no experience in public office as unlikely.

"No, but if you look back on the history of this country, Dwight Eisenhower was a national hero and a great hero and U.S. Grant was a national hero," he said.

"So I think it is extremely unlikely that anyone will be elected president who hasn't held elected office."

Pataki has repeatedly hit Trump on his controversial comments about Mexican immigrants during his announcement speech in June. He's called on the entire field to denounce Trump over those comments.

While Trump continues to rise in the polls, Pataki typically scores no higher than 1 percent in national polling.