Robert S. Mueller III was greeted with near universal praise when he was appointed to lead the investigation into possible coordination between the Trump campaign and Russia during the 2016 election, but as he builds his special counsel team, his every hire is under scrutiny.

At least seven of the 15 lawyers Mueller has brought on to the special counsel team have donated to Democratic political candidates, five of them to Hillary Clinton — a fact that President Trump and his allies have eagerly highlighted. These critics also point to some of the lawyers’ history working with clients connected to the Clintons and Mueller’s long history with former FBI director James B. Comey as they question whether those assigned to the investigation can be impartial.

Many lawyers and ethics experts say they can see no significant legal or ethical concerns with the team’s political giving or past work, and they note that Trump often misstates the facts as he casts aspersions. But others say the optical problem is a real one that threatens to undermine public confidence in the probe.

[Deputy attorney general appoints special counsel to oversee probe of Russian interference in election]

“In my view, prosecutors who make political contributions are identifying fairly strongly with a political party,” said William P. Barr, who served as attorney general under George H.W. Bush. “I would have liked to see him have more balance on this group.”

Criticizing those conducting an investigation is not a new tactic: Democrats famously put Independent Counsel Kenneth W. Starr in the crosshairs during his examination of President Bill Clinton. And by raising questions about the investigators early, legal analysts said, Trump is laying the groundwork to question any results that are not to his liking.

“By staking out the position of partisanship through campaign contributions, the president simply is setting a stage for a public relations assault down the road,” said Jacob Frenkel, a defense lawyer at Dickinson Wright who previously worked in the now-defunct Office of the Independent Counsel.

Trump has called the special counsel’s investigation the “single greatest WITCH HUNT in American political history,” adding that it was “led by some very bad and conflicted people!” In a more recent interview on Fox News, the president said that Mueller was “very, very good friends with Comey, which is very bothersome,” and that “the people that have been hired are all Hillary Clinton supporters, some of them worked for Hillary Clinton.”

“I mean the whole thing is ridiculous, if you want to know the truth from that standpoint,” Trump said. “But Robert Mueller’s an honorable man and hopefully he’ll come up with an honorable solution.”

Asked if Mueller would have to recuse himself, he said, “We’re going to have to see.”

Trump supporters have raised similar concerns. Former Republican House speaker Newt Gingrich wrote on Twitter that Republicans were “delusional if they think the special counsel is going to be fair.” The pro-Trump group Great America Alliance released a video in which conservative commentator Tomi Lahren opined, “Only in Washington could a rigged game like this be called independent.”

But Attorney General Jeff Sessions, a strong Trump backer who has recused himself from the Russia probe, was more circumspect in an interview with “Fox & Friends” on Friday.

“Mr. Mueller is entitled lawfully, I guess at this point, to hire who he desires, but I think he should look for people who have strength and credibility by all people,” Sessions said.

Pressed on whether he had confidence in Mueller, Sessions said: “I feel confident in what he’ll do. That’s all I can say to you about that.”

Mueller has brought in 15 attorneys to work with him — among them former colleagues at the firm WilmerHale and veteran Justice Department lawyers, said Peter Carr, a spokesman for the Special Counsel’s Office. Only 13 have been publicly identified.

Put together, the team is a formidable collection of legal talent and expertise with experience prosecuting national security, fraud and public corruption cases, arguing matters before the Supreme Court and assessing complicated legal questions.

The team members include Michael Dreeben, a Justice Department deputy solicitor general who has argued more than 100 cases before the Supreme Court; Andrew Weissmann, the chief of the Justice Department’s fraud section; James Quarles, who worked as an assistant special prosecutor on the Watergate Special Prosecution Force; and Jeannie Rhee, a former deputy assistant attorney general in the Office of Legal Counsel who also came from WilmerHale.

Rhee was on the team representing the Clinton Foundation, and another lawyer working with the special counsel, Aaron Zebley, once represented Clinton aide Justin Cooper. Zebley was Mueller’s chief of staff when Mueller served as FBI director.

Carr confirmed to The Washington Post that Brandon Van Grack, a Justice Department national security division prosecutor; Rush Atkinson, a trial attorney in the fraud section; and Andrew D. Goldstein, who had headed the public corruption unit in the U.S. Attorney’s Office in the Southern District of New York; and Zainab Ahmad, an assistant U.S. attorney in the Eastern District of New York specializing in terrorism cases, also had been assigned to work with the group. Goldstein had worked in the office under U.S. Attorney Preet Bharara, who was fired by Trump after he refused to resign upon request and who has said publicly that he had unusual exchanges with the president. Ahmad was recently profiled by the New Yorker for having prosecuted 13 terrorism cases without a single loss.

Seven special counsel team members have donated to Democratic campaigns — five of those to Clinton’s — and their giving totals nearly $53,000. The other six that are publicly known to be on the team did not give any political contributions, records show.

Ethics experts said the giving should not preclude anyone’s participation. Justice Department policies and federal law actually prohibit discriminating based on political affiliation when it comes to hiring for nonpolitical positions — meaning Mueller might feel he cannot consider donation history when he makes hires.

“Bottom line is, I don’t see how donations are relevant,” said Richard Painter, who was the ethics lawyer for President George W. Bush. “I’ve never heard of a single case where a prosecutor has been removed because of a political donation.”

[The White House may claim Mueller has conflicts of interest. Oh, the irony.]

Quarles’s donations were the most substantial. Over two decades, he gave more than $30,000 to various Democratic campaigns, including $2,700 to Clinton’s in 2016. But Quarles has also given to Republicans, contributing $2,500 in 2015 to Rep. Jason Chaffetz (R-Utah), chairman of the House Oversight Committee, and $250 to then-Sen. George Allen (R-Va.) in 2005.

Rhee donated nearly $12,000 to various Democratic campaigns, including President Barack Obama’s and Clinton’s, and Weissmann donated at least $6,600. Goldstein donated $3,300 to Obama’s campaigns. Three others — Van Grack, Atkinson and Elizabeth Prelogar, a lawyer in the Solicitor General’s office — donated less than $1,000 between them.

Some experts said Trump’s assertions — many of which misstate the facts — provide no real basis to question the team’s work.

“There’s a bipartisan consensus that the various, wild conflicts allegations that have been made by Trump and his allies are groundless,” said Norm Eisen, a fellow at the Brookings Institution who served as Obama’s ethics czar. “It just is not the case that lawyers or investigators are disqualified by political activity of this kind.”

Trump and his allies have also fixated on the longtime professional relationship between Mueller and Comey, but the president might be overstating their relationship.

The two men played central roles in a 2004 incident during the George W. Bush administration that has entered Washington lore, when both prepared to resign instead of go along with the reauthorization of a controversial surveillance program. The episode became particularly famous for Comey’s intervention at the hospital bed of then-Attorney General John Ashcroft.

Comey could be a key figure in Mueller’s investigation. The special counsel’s probe includes a look at whether Trump attempted to obstruct justice in possibly trying to shut down the investigation of former national security adviser Michael Flynn. Comey’s firing might be considered a piece of evidence in that case.

Ethics experts said they see no reason Mueller — who is registered as a Republican — would have a conflict. And David N. Kelley, Comey’s attorney, disputed Trump’s characterization of his client and Mueller’s connection.

“Bob and Jim have a congenial relationship as former colleagues. Both served long legal careers that involved overlapping time spent within the Department of Justice, and that’s pretty well documented. But beyond that, they’re not close, personal friends,” Kelley said. “They’re friends in the sense that co-workers are friends. They don’t really have a personal relationship.”

Kelley said Comey had never been to Mueller’s home, and Mueller had never been to Comey’s home. He said they had lunch together once and dinner together twice — once with their spouses and once after Comey became FBI director so Mueller could brief him on the job. Once, in 2004 with two others from the Justice Department, they played golf together, Kelley said.

Kelley said Deputy Attorney General Rod J. Rosenstein knew of Mueller and Comey’s relationship before naming Mueller as the special counsel. Rosenstein himself was appointed by Trump.

“I don’t think Jim has given it a lot of thought, but why would Bob be conflicted?” Kelley said. “Bob’s not conducting an investigation where Jim is pitted against a target of the investigation. If anything, he’s a witness.”

Mueller also has professional connections, and some of those are allied with Trump.

Although he resigned to take the special counsel job, Mueller had worked for the law firm WilmerHale, whose lawyers represent Trump’s former campaign chairman, Paul Manafort; Trump’s daughter Ivanka; and the president’s son-in-law, Jared Kushner.

Justice Department ethics experts ultimately cleared him to lead the probe despite that, and Carr said they gave the same consideration and approval to others from his firm.

Sari Horwitz contributed to this report.