Sen. Jeff Flake, R-Ariz., listens as President Donald Trump speaks before hosting a lunch with Senate Republicans in the Roosevelt Room of the White House in Washington, DC on Tuesday, Dec. 05, 2017.

"I don't see that happening in my case," he said. "I will give a speech in New Hampshire tonight. But just if nothing else, in memoriam of what a Republican Party should be."

"I've said that I do hope that somebody else runs in the Republican primary," Flake said at the Forbes 30 Under 30 event in Boston. "This is — the Republican Party is the president's party right now. But it won't always be. And it can't be if we're going to be a major political force in the future."

The retiring Trump critic's comments came even as he heads to New Hampshire, the nation's first primary state, for the second time this year. He is fresh off a dramatic political moment on Friday, when he joined Democrats and a couple other Republicans in calling for Senate leaders to delay a vote on Supreme Court nominee Brett Kavanaugh while the FBI investigates sexual misconduct accusations against the appeals court judge.

Sen. Jeff Flake hopes President Donald Trump will face a primary opponent in 2020. The Arizona Republican just doubts he will challenge the president himself, he said Monday.

The senator has tried to build a brand as a conservative with a conscience during Trump's chaotic first term, and cast himself as a potential alternative. Flake has slammed the president's attacks on the press and his immigration and tariff policies. While he has voted against Trump's priorities more than most of his GOP colleagues, he remains a conservative, voting with his party on its tax plan and an Affordable Care Act repeal bill.

Flake would have a difficult task gaining any traction in a Republican primary against Trump. Republican midterm primary voters showed their loyalty to the president by punishing some candidates who bucked him and boosting others who tied themselves closely to him.

Flake's stances have angered many Trump supporters, and the president himself supported a primary challenge against the senator before he announced his retirement. Last year, Trump called Flake "toxic" and "WEAK on borders, crime and a non-factor in the Senate."

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Flake was at the center of a dramatic Senate moment on Friday. In the morning, he announced he would support Kavanaugh, only hours after the judge and his sexual assault accuser, Christine Blasey Ford, appeared before the Senate Judiciary Committee in dramatic testimony.

After Flake's announcement, two women who said they were assaulted confronted the senator in the Capitol and pressed him about why he backed Kavanaugh. Immediately after at a Judiciary Committee meeting, he visibly frowned and looked down at the table in front of him.

He later left the main meeting room to confer with Democratic colleagues, then came back in and called for a delay in Kavanaugh's confirmation vote before the full Senate to allow for an FBI investigation. Trump subsequently ordered a supplementary background check related to the misconduct accusations.

In an interview on the CBS program "60 Minutes" that aired Sunday, Flake said there was "not a chance" he could have agreed to the compromise deal if he was running for re-election this year.

Flake speaks at the New Hampshire Institute of Politics at Saint Anselm College on Monday night. During his first stop in the Granite State this year, Flake said, "It has not been in my plans to run for president, but I have not ruled it out."

He is among a handful of Republicans who have fueled speculation about a Trump primary challenge. Others include Ohio Gov. John Kasich and Sen. Ben Sasse, R-Neb.