Flake, one of the GOP's most outspoken Trump critics, is stoking speculation about his 2020 plans with a Friday appearance in New Hampshire as part of the "Politics & Eggs" speaker series, which draws presidential hopefuls to the first-in-the-nation primary state.
Asked if he thought another Mr. Trump should receive a primary challenge, Mr. Flake replied, "Yes, I do".
"I mean, it would be a tough go in a Republican primary".
Flake abandoned his re-election bid past year because, he said, he did not want to compromise his integrity to try to win over pro-Trump voters in Arizona's August 28 Republican primary.
'Iran, Iran, Iran': In Fox interview, Netanyahu identifies greatest threat to Israel
The Iran nuclear deal was agreed to during the Obama administration. Another round of talks is expected to begin on Thursday in Berlin.
Trump frequently attacked multilateral trade deals as a presidential candidate, contending that "unfair" trade relationships with allies have hurt US workers and citing hefty USA trade deficits as evidence.
Trump spoke of his party's tax reform bill ("bigger than [Ronald] Reagan"), Rep. Maxine Waters (D-Calif.) ("very low-IQ individual"), NBC's Chuck Todd ("sleeping son of a bitch"), and Oprah, whom he said he would "love to beat" in the 2020 election, though it would be "a painful experience for her". "But that's not to say it will stay that way". "Somebody who voices, you know, reservations about where the president is or criticizes his behavior ... it's tough to be re-elected in a Republican primary".
He added: "I also think that there will be an independent challenge, particularly if the Democrats insist on putting somebody up from the far left of the party".
On Meet the Press, Flake said "tariffs are awful" for the economy and "tariffs married to uncertainty is probably even worse", referring to Trump's suggestion that he may allow certain exemptions and the possibility that the president may impose other tariffs.
"The risk is that this becomes normalized and we take as normal what is abnormal", Flake said of Trump's criticisms of the media.
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