Gilbert, Arizona (CNN) Sen. Jeff Flake -- who weeks ago published a book accusing President Donald Trump of having a corrosive impact on the Republican Party -- was eager to talk about anything but the President on Monday, one day before Trump visits Arizona for a campaign-style rally.

After an East Valley Chambers of Commerce breakfast, Flake deflected reporters' questions about Trump's tweets that he is "a non-factor in the Senate" and "toxic!"

"I don't worry about it at all," he said.

Flake also wouldn't directly answer questions about whether Trump is right to seemingly endorse his primary challenger in his 2018 re-election bid. Trump, who has long criticized Flake and mused last year about spending $10 million of his own money to unseat him, praised Kelli Ward, a conservative former state senator who is already running against Flake, in a tweet last week, saying it is "great to see" that she is running against Flake.

"That's not my realm. That's somebody else's. I just -- I'm running my own campaign. It's going well. And what the President does, that's his prerogative," Flake said.

Flake also wouldn't say whether Trump should pardon controversial former Maricopa County Sheriff Joe Arpaio during his visit to Phoenix.

"That's his choice to make," Flake said.

Flake's public schedule has been sparse since he kicked off the August recess -- and his 2018 re-election bid -- by publishing a book, "Conscience of a Conservative," in which he is sharply critical of Trump's style of politics.

He kept from mentioning Trump's name Monday morning, but warned that the GOP should not "follow the lead of some individuals who would give in to that kind of destructive behavior."

He also complained of a national political environment in which compromise is frowned upon.

"With this vitriol that we have, with this inability to compromise, in my view, as a conservative, it is preventing us from achieving conservative ends. ... It's disheartening to be in that situation where you're attacked because we need a bipartisan solution for something."

Trump will be in Arizona on Tuesday for a night-time rally in Phoenix. In addition to Trump's tweeted praise for Ward, the White House has kept up an ongoing dialogue with at least two other potential candidates.

The closest Flake got to directly confronting Trump was over free trade, with the Arizona Republican telling the crowd Monday morning he is "concerned that the party is going down a populist route."

Flake said the United States is "going to be left behind" if it turns away from trade deals, including the Trans-Pacific Partnership -- from which Trump's administration withdrew earlier this year.

He called it "a big mistake which will haunt us for a long time," adding that the withdrawal could carry geopolitical consequences because it gives China, which is not part of the TPP negotiations, an opportunity to exert its influence.

"Those countries in Southeast Asia -- we want them to be in our trade orbit, not just China's trade orbit. And we're giving them little choice now," Flake said. "We have to get away from the idea that we're the only game in town, because we're not."

Flake also said the United States must remain in the North American Free Trade Agreement

"I'm concerned that the early rhetoric of the President's campaign was to reject NAFTA -- to rip it up," Flake said, adding that the administration's efforts to renegotiate the pact with Mexico and Canada "look better."

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Flake said he sees the administration's efforts to reduce the number of undocumented immigrants crossing into the United States via the Southern border -- a downward trend in recent years, he said -- as imperiled by Trump's brash talk about leaving NAFTA, which he fears would jeopardize Mexico's economy.

"That's one of the concerns I have about where we're going on trade -- the other implications it has on border security," Flake said.

Flake, who has generally toed the party line with Trump and the Republicans on Senate votes, credited Trump for his appointment of Supreme Court justice Neil Gorsuch and his regulatory rollbacks, as well as his national security team.

"I think that the national security team that the President's put together is a good one. I sleep better at night knowing that Gen. Mattis is in charge," Flake said, referring to Defense Secretary James Mattis.

Flake waded briefly into health care -- where the GOP's effort to repeal Obamacare was thwarted in part by Arizona's other Republican senator, John McCain . He said the effort should move back to the committee level.

He also said Monday that lawmakers are "feeling the pressure" on tax reform, and should lower the corporate income tax rate.

"It's a heavy lift, there's no doubt," Flake said. "Every tax credit, every deduction, every tax earmark -- there's a constituency for all of that out there. And believe me, they come and lobby hard. So it's not going to be easy by any stretch."

Flake touched briefly on the investigations into Russian election meddling proceeding in House and Senate committees, as well as at the Justice Department, where special counsel Bob Mueller is overseeing the probe.

"Russia did try to intervene in our election," Flake said. "Whether they were successful or not, we'll leave it to others, but they certainly tried. And we ought to want to know what they did and we ought to try to make sure that doesn't happen again here or in other countries, as well."