Wray worked in the Department of Justice during President George W. Bush's administration from 2003 until 2005.
Wray says he has not been asked to pledge his loyalty to the White House nor would he do so.
After Mr Trump declared his beleaguered son to be innocent, Christopher Wray told senators that anyone approached by a foreigner offering help to sway United States elections should have reported the encounter.
Wray also said he did not believe Mueller's investigation to be "a witch hunt", as Trump has said a couple of times on Twitter.
Wray made this assessment after revelations this week that the president's son, Donald Trump, Jr. had met past year with a Russian lawyer whom he believed would give him damaging information about Hillary Clinton. He replied that he had not and that the only meeting he had on the topic was one with Deputy Attorney General Rod Rosenstein at which Rosenstein "made the observation" that the appointment of Robert Mueller as special counsel to investigate the matter, an act in which Rosenstein was instrumental, "made for a better landscape for me to consider taking on this position".
"My preference and my presumption.there should be other people in the room", Mr Wray said. "And that's what I promised you I would do, and that's what I did".
Mr. Wray bore a special responsibility to assure lawmakers and the public that he would support a fair investigation into the administration of the man who appointed him, resisting any bullying or blandishments.
Graham asked whether Trump Jr. should have agreed to that meeting; Wray stopped short of answering. "Faithful to our laws", Wray said. "I'm looking around and feeling that you had a good hearing today", said Sen.
His opening remarks underscored the concerns Senators have about his ability to be an independent leader, resistant to political pressures including from the White House, are expected to dominate his hearing Wednesday before the Senate Judiciary Committee to become the FBI's eighth director.
Senator Patrick Leahy said that they have now learned that a number of members of the Trump campaign were eager to work and talk with members of the Russian organisation, even though they're an adversary of ours, about the campaign.
When asked if he would support the notion of creating a cyber unit with Russian Federation to protect elections from hacking, Wray said he would not support doing anything that "was putting us at greater risk as opposed to greater protection".
And when asked by Graham about emails released Tuesday showing Trump Jr. was willing to take help from Russian Federation during the campaign, Wray said any foreign efforts to meddle in an election should be reported to the Federal Bureau of Investigation, not accepted.
Wray said a loyalty pledge was not part of his nomination process.
Now a partner at a private law firm, Wray also defended Mueller and the character of the special prosecutor. Wray also represented New Jersey Governor Chris Christie in a political scandal. "Period", Wray told senators.
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