The president appointed Wray in 2017 following the firing of James Comey. Since then, Wray, who is his style, has largely kept a lower profile than his predecessor, and he has sought to distance himself and the agency from former leaders who oversaw the start of the 2016 investigation into Russian election interference and ties to the Trump campaign.
The FBI has said that during Wray, the agency has cooperated with several investigations into the FBI's handling of the Russia probe over which Trump remains upset. Wray also enjoys a good relationship with Barr, who has privately conveyed that support to Trump, according to an administration official.
But a review of the Flynn case by U.S. Attorney Jeffrey Jensen has contributed to criticism from the president and his supporters, not only from the agency, but also from Wray.
In recent weeks, the Department of Justice gave Flyn's lawyers a cache of documents that appeared in conservative media stories that claimed that FBI corruption was at work in the investigation of Trump's former national security adviser. That led to a tide of calls for Wraye's firing from prominent Fox News hosts, whom the president is known to watch.
On Friday, Trump clarified his displeasure with Wray in a call for the Fox News morning show.
"Well, a lot of things are going to be told over the next few weeks, and let's see what happens," Trump said when asked about Wray. "He was appointed by (former Attorney General) Rod Rosenstein."
The president continued a scathing criticism of Wray, not quoting details of what the FBI director has done wrong, saying, "Let's see what happens to him. Look, the jury is still out on it, but there had been a lot easier if he came out instead of skirting and went through 19 different ways, except through the FBI. "
The conservative criticism of Wray over the Flynn case reached such a point in recent days that the FBI sent an unusual statement defending the director.
"Under Director Wray's leadership, the FBI has cooperated fully and been transparent with the review conducted by U.S. Attorney Jeff Jensen, just as it has with U.S. Attorney John Durham and was with Inspector General Michael Horowitz. As for certain documents in Michael The Flynn case from the period 2016-2017 which is now the subject of reporting from the press, the FBI has previously produced these materials to the Inspector General and United States Attorney Durham, "the FBI said.
"Director Wray is still committed to addressing the mistakes of former FBI leadership while maintaining the basic principles of rigor, objectivity, accountability and ownership in fulfilling the Special Unit's mission of protecting the American people and defending the Constitution," the FBI added .
Barr has been trying to come to Wraye's rescue, giving several rebuttals in recent months to other conservative allies by the president who have heightened criticism of the FBI director.
In interviews, Barr has been quick to point out that Wray has cooperated with several investigations Barr has ordered in the FBI's handling of sensitive cases, including the probes run by Durham and Jensen, which are often awarded for political points by Trump.
"He has been a great partner to me in our efforts to restore the American people's confidence in both the Department of Justice and the FBI," Barr told CBS News on Thursday.
Barr also tried Thursday to protect Wray from attacks that the FBI had withheld the recently disclosed documents, including internal emails and meeting remarks, that supported the Justice Department's return to the Flynn case.
"There are many cases in the Department of Justice, and I do not consider it the responsibility of the director to make sure all the documents are produced in each case," Barr said.
Wray has tried to distance himself from the controversy surrounding Comey, his predecessor, and in the first few months at the top of the agency replaced executives who had consisted of Comey's management team.
He also moved swiftly to condemn and take corrective action after the Department of Justice's inspector general revealed last year that Comey FBI officials had made a series of mistakes when trying to identify a member of Trump's campaign as part of the Russia investigation.
"I am not someone – as it is now clear to many people – who expresses themselves with hyperbole and high rhetoric. I am someone who reflects his views through action," Wray testified in February to a House panel.