Washington (CNN) Arizona Republican Sen. Jeff Flake called on members of his party to stand together and criticize President Donald Trump's behavior shortly after announcing he would not seek re-election.

"We Republicans certainly can't countenance that kind of behavior," Flake said on CNN's "The Lead with Jake Tapper."

Flake continued, "We ought to stand up and say, 'This is not right. This is not us. This is not conservative.'"

Flake earlier Tuesday said he would not seek re-election, and in a speech on the Senate floor, the now-outgoing senator issued sweeping criticism of the President, with whom he has long tussled.

Tough running against Trump

After his announcement, White House press secretary Sarah Sanders said it is "probably a good move" for Flake not to seek re-election, nodding to the electoral rift between him and Trump, who has met with several potential Republican primary challengers to the senator.

Flake said he had "no response" to the comment, but made clear in the interview he thought his opposition to the President would have hurt him in Arizona's Republican primary.

"There is just a very narrow path for a Republican like me in today's Republican Party to get the nomination," Flake said. "I would have to run a campaign that I couldn't be proud of, frankly, to win re-election."

Flake said he accepts that the current political climate means most Republican voters do not feel the same way he does and that they would condone the President's controversial actions, but predicted "history" would look kindly on his choice.

"I think that this fever will break, but I don't know that it will break by next year," Flake said.

Flake said he felt there could be parallels to the tide of opposition that brought down Wisconsin Republican Sen. Joseph McCarthy in the 1950s, and that it would take such a culmination of outrage to push Trump to change.

"When enough people say, 'This is enough. We expect different behavior from our commander-in-chief and the President of the United States,' then it will change," Flake said. "But it hasn't yet."

No pivot from Trump

Flake, who has a conservative voting record, said what "troubled" him about Trump was his behavior, controversial actions and past endorsement of the racially charged "birther" theory about former President Barack Obama.

The Arizona senator said he believed Trump was setting a bad example for children, and praised Tennessee Republican Sen. Bob Corker, a former ally of Trump turned opponent who also has announced he would not seek re-election , for his values.

"I've known Bob Corker for a long time, and he's a man of integrity who stands for what he believes," Flake said.

He said he did not fault his GOP colleagues who have not spoken out about the President, but added that many people have been waiting for Trump to change, and he does not see any change coming.

"We keep waiting for a pivot that simply isn't happening," Flake said. "And I think that we can't wait any longer."

2020 'a long time away'

But Flake demurred when asked about his next steps, declining to say whether he or someone else should challenge Trump in 2020.

"I won't go there," Flake said. "That's a long time away. ... It's early."

The senator said there is plenty he still wants to get done in the Senate in the meantime, adding that he had some overlap with Trump on a number of issues. He cited Trump's expressed desire for Congress to establish legal protections to prevent young, undocumented immigrants from being deported as an issue on the top of his mind -- one he thought he and Trump saw eye to eye on.

"There are many things that we agree with that we can work together on," Flake said.

Flake also talked up the importance of reforming the authorization for use of military force, which Congress passed nearly unanimously in 2001 and has left standing as the war on terror has continued.

"Going since 2001 without a new authorization for use of military force is really an abdication of our authority," Flake said.