WASHINGTON (Reuters) - Republican U.S. Senator Jeff Flake, who has not ruled out running against Donald Trump for the White House, on Sunday criticized as a "diversion tactic" the president's unsubstantiated allegation last week of an FBI "spy" being planted in his election campaign.

Flake's comments, on NBC's "Meet the Press," put him again at the forefront of very few Republican lawmakers willing to openly challenge Trump over his attacks on law enforcement officials who are investigating Russian meddling in the 2016 U.S. election and possible collusion by the Trump campaign.

The investigation was begun by the FBI in July 2016, but handed over by the Justice Department to Special Counsel Robert Mueller in May 2017 after Trump fired FBI Director James Comey.

Flake said Trump's unfounded allegations about FBI spying on his campaign, which the president has called "Spygate," came amid escalating, behind-the-scenes concern in the U.S. Senate that the president may try to stop the probe by firing Mueller or the person who appointed him, Deputy Attorney General Rod Rosenstein.

 

"The president had this diversion tactic, obviously, with so-called Spygate," Flake said of Trump's assertions last week. "There is concern that the president is laying the groundwork to move on Bob Mueller or Rosenstein. If that were to happen, obviously, that would cause a constitutional crisis."

Some senior Republicans, including Flake, have sounded similar warnings in recent weeks as the Mueller investigation has plowed forward, drawing frequent denunciations from Trump.

Mueller is also investigating any possible obstruction of justice by Trump. Trump and the White House have repeatedly denied any collusion by the campaign, or any other wrongdoing.

The White House has also said it is not considering firing Mueller.

In a tweet on Sunday, Trump called the investigation a "phony Russia Collusion Witch Hunt" - reiterating his oft-stated resentment at the probe that has clouded his presidency.

After Trump demanded an inquiry into his "spy" claim, the current FBI Director Christopher Wray and Rosenstein, who oversees Mueller’s probe, held two classified briefings on Thursday for senior lawmakers of both parties on the matter.

Democratic Representative Adam Schiff was among those briefed. Speaking on ABC's "This Week" on Sunday, he said, "There is no evidence to support that spy theory. This is just a piece of propaganda the president wants to put out and repeat."

Republican Senator Marco Rubio told the same program that so far he has seen no evidence to support the president's assertions about a campaign "spy."

"What I have seen so far is an FBI effort to learn more about individuals with a history of bragging about links to Russia that pre-exist the campaign. If those people were operating near my office or my campaign, I'd want them investigated," said Rubio, who ran unsuccessfully against Trump in the 2016 Republican presidential primary campaign.

"If it turns out to be something different, we want to know about it. But it is the FBI's job to investigate counterintelligence," Rubio said.

U.S. intelligence agencies concluded in January 2017 that Russian President Vladimir Putin ordered an effort to meddle in the U.S. election campaign, included seeking to help Trump win. Moscow has denied the charge.

Flake delivered a blistering attack on the president when he announced last October he would not run this year for re-election to the Senate. Asked if would run for the White House in 2020, he said: "It's not in my plans, but I've not ruled anything out. I do hope that somebody runs on the Republican side other than the president, if nothing else simply to remind Republicans what conservatism is and what Republicans have traditionally stood for."

(Reporting by Kevin Drawbaugh; Editing by Frances Kerry)