Republican Senator Jeff Flake unleashes a fierce broadside against President Donald Trump, as he announces he would not seek re-election.

Republican US Senator Jeff Flake, invoking the 1950s demagoguery of Senator Joseph McCarthy, says "you can't continue to just remain silent'' about US President Donald Trump's politics and behaviour.

"There is a tipping point. ... I hope we're reaching that tipping point,'' Flake told NBC's Today.

The Arizona senator has made the rounds of morning television news shows in the US to talk about his decision not to run for re-election in 2018 and his impassioned speech on the Senate floor on Tuesday (Wednesday NZ Time), in which he said he could no longer be "complicit'' with the Republican president.

REUTERS Republican Senator Jeff Flake says it's time for his colleagues to stand up to US President Donald Trump.

"We are excusing undignified and outrageous and reckless speech and behaviour as 'telling it like it is'. That's not right,'' Flake said on Wednesday (Thursday NZT) on MSNBC.

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REUTERS Tensions among Republicans about President Donald Trump boiled over as two senators accuse Trump of debasing US politics and the country's standing abroad.

Trump immediately fired back on Twitter, saying that Flake and another retiring Senate Republican, Bob Corker of Tennessee - who had criticised Trump on Tuesday as "untruthful'' and debasing the nation - aren't running for re-election because "they had zero chance of being elected''.

He also contended that Flake and Corker stood alone, boasting in several tweets that he had received standing ovations at a Senate Republicans' luncheon on Tuesday (Wednesday NZT) at the Capitol.

Flake cited the era of McCarthy, the Republican Wisconsin senator whose smear tactics alleging Communist infiltration ultimately led to his censure. In an op-ed column in The Washington Post, Flake quoted Joseph Welch, a US Army lawyer, who stood up to McCarthy in a June 1954 hearing and demanded: "Have you no sense of decency, sir?''

KEVIN LAMARQUE/REUTERS US President Donald Trump has been arguing with Republican senators on Twitter.

"The moral power of Welch's words ended McCarthy's rampage on American values, and effectively his career as well,'' Flake wrote. "We face just such a time now. We have again forgotten who we are supposed to be.''

Flake also said he thinks more of his Republican colleagues will speak out.

"It's up to us to stand us and say, 'This is not acceptable','' he told ABC's Good Morning America.

Asked why others in his party haven't yet done so, Flake said, "There is some fatigue about it.''

Flake stopped short of saying Trump should be declared unfit for office or impeached.

"The voters made their choice,'' Flake said. "He was elected fair and square.''