Deputy Attorney General Rod Rosenstein talks to an aide on Capitol Hill in Washington, Tuesday, June 13, 2017, while testifying before a Senate Appropriations subcommittee hearing on the Justice Department's fiscal 2018 budget. Rosenstein said he has seen no evidence of good cause to fire the special prosecutor overseeing the Russia investigation. (AP Photo/Alex Brandon)

Deputy Attorney General Rod Rosenstein talks to an aide on Capitol Hill in Washington, Tuesday, June 13, 2017, while testifying before a Senate Appropriations subcommittee hearing on the Justice Department's fiscal 2018 budget. Rosenstein said he has seen no evidence of good cause to fire the special prosecutor overseeing the Russia investigation. (AP Photo/Alex Brandon)

WASHINGTON (AP) — Criticism of special counsel Robert Mueller used to be off limits. No more.

Some of President Donald Trump’s closest allies — including one of his sons — have begun questioning whether Mueller’s wide-ranging probe is becoming too political, as the investigation into Russian meddling in the 2016 election intensifies. The White House finally said Tuesday evening that Trump has “no intention” of firing Mueller, amid speculation and concern that he was weighing that option.

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The effort to muddy the waters surrounding the investigation is coming amid growing White House concern that the probe could detract from the president’s agenda for months or years to come. Senators on Tuesday questioned both Attorney General Jeff Sessions and Deputy Attorney General Rod Rosenstein on how the inquiry is being handled.

Until now, Mueller had drawn widespread praise from Republicans and Democrats alike. Trump, who isn’t typically shy about leveling criticism, especially on Twitter, hasn’t commented on the longtime former FBI director. And leading Republican legislators on Tuesday waved off the idea of firing Mueller, with House Speaker Paul Ryan saying that his advice was to “let Robert Mueller do his job” and Senate Majority Leader Mitch McConnell voicing confidence in the special counsel.

But expressions of discontent with Mueller are bubbling up nonetheless.

Former House Speaker Newt Gingrich led one line of attack with a tweet that said “Republicans are delusional if they think the special counsel is going to be fair.” He added that fundraising records show some of the lawyers whom Mueller selected for his team have contributed to Democrats.

“It makes sense to point out any level of bias, to highlight any biases inherent in Mueller and this probe in order to force him to be transparent,” Gingrich said. He said Trump had called him Monday night and the two discussed Gingrich’s concerns about the probe.

Tuesday morning, Trump supporter Ari Fleischer, who served as President George W. Bush’s press secretary, again highlighted the issue of Mueller’s probe being handled by attorneys who have donated mostly to Democrats, a message that Donald Trump Jr. quickly retweeted to his own 1.7 million followers.

Peter Carr, a spokesman for Mueller, declined to comment on the issues Gingrich and others have raised. In general, it is impermissible to ask prospective government hires about their political leanings, including whether they’ve made donations.

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Both Fleischer and Gingrich had previously vouched for the character and integrity of Mueller, who was appointed FBI director by Bush and whose term was extended an extra two years by Democratic President Barack Obama.

Anxiety about the probe — and fresh concerns about the political leanings of some of the attorneys involved — is percolating in the West Wing of the White House.

Chris Ruddy, a Trump friend and the CEO of the conservative website Newsmax, raised the possibility of the president considering terminating Mueller, a potentially explosive option.

White House officials said late Monday that Ruddy was at the White House that day, but said he hadn’t meet with the president and never spoke with him about the issue.

Still, it took until Tuesday night for the White House to actually dispute Ruddy’s suspicion.

On Trump’s plane ride home after a trip to Wisconsin, Sarah Huckabee Sanders told reporters he “has no intention” of firing Mueller, even though she maintained that “the president has the right to.”

A person close to Trump’s legal team said earlier Tuesday that there have been no discussions about firing Mueller with the legal team. The person spoke on condition of anonymity to discuss private conversations.

But Ruddy opened a new line of questions about Mueller’s impartiality — the fact that Trump had considered Mueller for the FBI director’s job before he was named special counsel.

Trump interviewed Mueller for the director’s position days before Rosenstein picked Mueller as special counsel for the Russia probe, Sanders confirmed Tuesday. The interview was first reported by PBS.

Other Trump supporters homed in on the sequence of Mueller’s job interviews.

Sam Nunberg, who worked for Trump’s presidential campaign, said it “could seem to be a conflict” for Mueller to first interview with the president to be a possible replacement for fired FBI Director James Comey and then days later to be named as the special counsel heading an investigation that could look into Comey’s firing.

But Stephen Gillers, a New York University professor who specializes in legal and judicial ethics, said the Mueller interview with Trump presented “no conflict whatsoever.”

It would be hard to make the case, he said, that the experience of interviewing for FBI director would make it impossible for Mueller to fairly exercise the broad discretion afforded to prosecutors.

Trump has repeatedly denied colluding with Russia during the presidential campaign, and Comey and others have testified that there is no evidence to the contrary. Still, Gingrich said any special counsel with an agenda can “all of the sudden find something procedural and technical to latch onto.”

With few exceptions, Trump’s allies are urging him not to move to dismiss Mueller, which would be both politically and technically complicated. Rosenstein would be the one to fire Mueller, which he repeatedly assured senators Tuesday he would not consider without “good cause.”

Rosenstein is charged with Mueller’s fate because Attorney General Jeff Sessions recused himself from all matters having to do with the Trump-Russia investigation. Sessions told senators on Tuesday that he’d recused himself because he was part of Trump’s campaign.

Gingrich and Ruddy said it would be a “mistake” for Trump to remove Mueller, although both said they see the probe as unnecessary.

Barry Bennett, a GOP strategist who served as an adviser to Trump’s campaign, said he believed it would be too damaging for Trump to try to remove Mueller, but that he had concerns about the appearance that the probe was being politicized.

“I think that he should be more cognizant of making sure that the people who come to work with him are non-partisan, for his own credibility,” Bennett said of Mueller. Still, he said: “Bob Mueller did a great job as FBI director. I don’t question his integrity at all, but he has to be careful not to create the impression of partiality.”