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GOFFSTOWN, N.H. — In a head-turning visit to this early voting state, retiring Sen. Jeff Flake of Arizona called for a fellow Republican to challenge President Donald Trump in the 2020 GOP primaries.

Flake said he had not ruled out the possibility that he could mount a 2020 bid himself — though, he noted, the "odds are long."

"I hope somebody runs, like I said, as a Republican, cause I think Republicans are yearning to hear a conservative message, traditional conservative message," Flake said after speaking at the Saint Anselm College's New Hampshire Institute of Politics "Politics and Eggs" speakers series event on Friday.

Flake said he has engaged in "conversations" with other Republican officeholders about the prospects of a GOP presidential primary challenger but that "nothing formal" is in the works.

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The Arizona senator opted against running for re-election for a second term to the U.S. Senate this year amid questions about his own ability to fend off challengers in the state's Republican primary. But he suggested he could potentially become a more attractive candidate down the road if the party loses more races like the special election this week in Pennsylvania's 18th Congressional District, where the party came up short despite Trump's 20-point winning margin there in 2016.

"Right now, this is the president's party," Flake said. "Republican primary voters in Arizona and elsewhere are firmly with the president — by large majorities. But I do think that will change. And as that changes, we'll see."

Flake's visit visit comes a week before President Trump and Vice President Mike Pence visit the Granite State. Outside of Ohio Gov. John Kasich, Flake is the most high profile Republican to have opened up the possibility of challenging Trump.

He released a book, "Conscience of a Conservative," last summer that asserted Republicans were engaged in "spasms of a dying party."

On Friday, he derided President Trump's "penchant for destruction."

"Perhaps what will be most remembered from this period will be the president's war on objective reality and the reflexive impulse to speak falsely," Flake said.

"The time a notion takes to tickle the cerebellum, send a signal to your fingers to pick up your phone and thumb type a tweet is not a comparable process" to crafting policy, he said. "We should know by now there is no strategic brilliance to marvel at here."

Flake said Republicans "have a long road to whole to recover as a party," and suggested a more formidable challenger to the president may come in the form of an Independent candidate in the 2020 general election — someone who could pull in a "huge swath of voters in the middle looking for something else."

Trump overwhelmingly defeated the large Republican field in the 2016 New Hampshire primary, garnering 35 percent of the vote. Ohio Gov. John Kasich finished second with 15 percent.

The New Hampshire crowd sat silently and attentively — outside of one brief collective chuckle at a joke — as Flake spoke, before giving him a standing ovation when he concluded his speech.

"I thought he had a great message out there of taking the high road," said Brendan Flaherty, a freshman at Saint Anselm college who attended the breakfast. "If he challenged Trump in the primary, he'd have my vote."