Former Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden Maybe they just don't like cowboys: The president is successful, some just don't like his style MORE (R-Ariz.) announced Tuesday morning that he would not run for the White House in 2020.

“I have always said that I do hope that there is a Republican who challenges the president in the primary. I still hope that somebody does, but that somebody won't be me. I will not be a candidate,” Flake said on “CBS This Morning.”

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Flake, a frequent critic of President Trump Donald John TrumpUS reimposes UN sanctions on Iran amid increasing tensions Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally MORE, had been floated as a possible 2020 contender to challenge the president for the Republican Party nomination.

You thought about running in 2020. Are you going to run?



"I have always said that I do hope that there is a Republican who challenges the president in the primary. I still hope that somebody does, but that somebody won't be me. I will not be a candidate." -- @JeffFlake pic.twitter.com/YX1LtXzEBX — CBS This Morning (@CBSThisMorning) January 29, 2019

“It’s a difficult path anyway. The [Republican National Committee] and the president’s campaign are now melded, they’re trying to do everything they can to squelch any opposition," Flake said.

"I still hope that some — and some are still talking about it — do run, I think that that’s healthy and I’m not a fan of this president. But that won’t be me,” he added.

Flake, in November, hadn't yet ruled out a run, emphasizing that someone in the party needs to run against Trump.

"I've not ruled it out. I've not ruled it in. Just, somebody needs to run," Flake told reporters at the time.

Flake, who supported many of the Trump administration’s policies during his tenure in the Senate, has had a contentious relationship with the president since the 2016 campaign, when Flake confronted the then-candidate for his criticisms of Sen. John McCain John Sidney McCainMomentum growing among Republicans for Supreme Court vote before Election Day McConnell urges GOP senators to 'keep your powder dry' on Supreme Court vacancy McSally says current Senate should vote on Trump nominee MORE (R-Ariz.).

Flake, during his interview Tuesday, added that he is joining CBS News as a contributor.

Former Ohio Gov. John Kasich (R), a frequent critic of Trump’s and considered by many to be a moderate, has been floated as a possible 2020 challenger to Trump. Kasich, who has already run for president twice, said in November that he was “very seriously” considering a White House bid.

Asked in November who else within the party should be in the "conversation" about a primary challenge to the president, Flake pointed to Kasich and Sen. Ben Sasse Benjamin (Ben) Eric SasseChamber of Commerce endorses McSally for reelection Ben Sasse is mistaken with idea for the election of senators in America Big Ten football to return in October MORE (Neb.).