Wray, nominated by Trump to replace the fired James Comey as FBI director, on Wednesday sought to establish independence, saying it would be "highly unlikely" he would agree to meet with him alone.
Wray appeared at his US Senate Judiciary Committee confirmation hearing amid an uproar over 2016 emails released on Tuesday involving the president's son.
The emails show Donald Trump Jr agreeing to meet a woman he was told was a Russian government lawyer with damaging information about Democratic rival Hillary Clinton as part of Moscow's official support for his father.
Wray deflected specific questions but said: "Any threats or effort to interfere with our election from any nation-state or any non-state actor is the kind of thing the FBI would want to know."
Wray, who appeared likely to win confirmation, said he had no reason to doubt US intelligence findings that Russia interfered with the election.
Trump fired Comey on May 9 and later cited the "Russia thing" as his reason.
Trump has called the Russia probe a "witch hunt" but Wray said he did not "consider Director Mueller to be on a witch hunt".
Comey has testified Trump asked him for loyalty.
Wray said he spoke with no one at the White House about Comey's firing.
"My loyalty is to the Constitution, to the rule of law and to the mission of the FBI. And no one asked me for any kind of loyalty oath at any point during this process, and I sure as heck didn't offer one," Wray said.
Comey also testified Trump pressed him in a one-on-one session to drop the FBI investigation into former national security advisor Michael Flynn's Russian ties and said he felt he was fired in a bid by the president to undercut the Russia probe.
Wray repeatedly vowed independence, saying he would be "faithful to the Constitution".
