A leading Republican critic of Donald Trump said on Sunday there was a “crying need” for someone in the party to challenge the president in 2020.

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“All I can say is I hope that somebody does challenge the president,” the Arizona senator Jeff Flake told CNN’s State of the Union. “There is a crying need out there for some Republicans to stand up and say this is not normal. This is not right.”

Flake, a conservative, will not stand for re-election in November and has emerged as a strident critic of Trump’s policies and behaviour. He has not ruled out a 2020 run himself. Other Republicans touted as potential rivals to Trump include the Nebraska senator Ben Sasse and Ohio governor, John Kasich.

“We want Republicans who will take the higher ground,” Flake said. “To see what’s going on right now in terms of the chaos and these actions that clearly are not conservative on tariffs and whatnot, it’s not just the policies but the behaviour as well.”

As Flake spoke, Trump was using Twitter to attack the fired FBI officials Andrew McCabe and James Comey, and Robert Mueller, the special counsel investigating Russian election interference and links between Trump aides and Moscow.

On Friday, Trump’s lawyer Michael Cohen threatened Stephanie Clifford, an actor in pornographic movies known professionally as Stormy Daniels, with $20m in damages if she breaks a $130,000 non-disclosure agreement about an alleged affair with Trump beginning in 2006. An interview with Clifford is due to be broadcast by CBS next Sunday.

“People want to remember the Republican party as the decent party and it is not right now and so what I’m seeing is there’s a crying need for that,” Flake claimed. “I don’t know who will step up in the end but I hope somebody does. I’m not ruling it out but I think the odds are long that I will end up doing it.”

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Flake also said he believed any move to fire Mueller, as advocated by Trump’s lawyer John Dowd on Saturday, would prompt concerted Republican opposition.

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Asked if a Republican primary run against Trump would be a moral stand rather than one with a realistic chance of success, Flake said: “Certainly right now nobody would defeat the president but certainly two years from now we could have a totally different scenario.

“Nothing focuses the mind like a big election loss and what might happen in the midterms is that big election loss. My friend Charlie Dent in the House said, this is a five-alarm fire, when you look at what happened in Pennsylvania politically.”

Conor Lamb, a Democrat, this week claimed victory in a Pittsburgh-area House district that went for Trump by 20 points, despite Trump appearing in person to support the Republican candidate, Rick Saccone.

“It would certainly be hard to defeat the president right now in a Republican primary,” Flake said. “This is the Trump party. I just am not sure that it will be two years from now.”