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Charles G. Koch, the billionaire industrialist, suggested in an interview Sunday that he was open to supporting Hillary Clinton for president and said it was possible she would make a better president than her Republican rivals.

It was an unexpected sentiment from Mr. Koch, who has for years deployed his vast wealth to champion conservative causes and Republican candidacies, emerging as a major foe of the Democratic Party.

But he was quickly rebuffed by Mrs. Clinton, who declared on Twitter that she was uninterested in Mr. Koch’s support.

In an interview with Jonathan Karl of ABC, which aired on “This Week with George Stephanopoulos,” Mr. Koch sounded at times baffled and disappointed by the language and ideas of several Republican presidential candidates.

He called a plan by Donald J. Trump to temporarily bar Muslims from entering the country “monstrous” and dismissed Senator Ted Cruz’s proposal to carpet-bomb territory held by the Islamic State as “frightening” hyperbole.

Mr. Koch spoke somewhat fondly of former President Bill Clinton, suggesting he held down government spending and regulation compared with his successor, President George W. Bush. He called Mr. Bush “a fine person, and tried to do the right thing but was misguided.”

That prompted a question about Mrs. Clinton. Below is a transcript of the ensuing exchange:

KARL: So is it possible another Clinton could be better than another Republican—

KOCH: It’s possible.

KARL: Next time around?

KOCH: It’s possible.

KARL: You couldn’t see yourself supporting Hillary Clinton, could you?

KOCH: Well, I— that— her— we would have to believe her actions would be quite different than her rhetoric. Let me put it that way. But on some of the Republican candidates we would— before we could support them, we’d have to believe their actions will be quite different than the rhetoric we’ve heard so far.

In a message on Twitter Sunday afternoon, Mrs. Clinton said she was “not interested in endorsements from people who deny climate science and try to make it harder for people to vote.”

Although she did not mention Mr. Koch by name, she linked to a message about his ABC interview. And her statement alluded to Mr. Koch’s record of opposing government efforts to mitigate climate change through regulation as well as to the Koch brothers’ support for an organization that is pushing states to adopt tougher voter ID rules. Democrats have long argued such rules are intended to make it harder for some Americans to vote.