Washington
Wray was nominated by Trump in June 2017 to succeed James Comey who was abruptly fired amid the Federal Bureau of Investigation's (FBI) probe into the the former President's campaign's link with Russia, Xinhua news agency reported.
While she was queried at her first White House briefing on Wednesday about Wray's position, Biden's Press Secretary Jen Psaki did not give a direct response, adding that she had not spoken with the the President about it "in recent days", The Hill news website reported.
But in a tweet on Thursday, she said: "I caused an unintentional ripple yesterday so wanted to state very clearly President Biden intends to keep FBI Director Wray on in his role and he has confidence in the job he is doing."
The FBI director is appointed to a 10-year term, but does not necessarily serve the full term and can be fired by the President or choose to resign.
It was not immediately knows if Wray and Biden has spoken since the latter was inaugurated on Wednesday as the new President.
The Hill news report quoted an FBI official as sayingthat all interactions between the Bureau and Biden's team have been "very positive".
Biden's decision on Wray was welcomed by House Intelligence Committee Chairman Adam Schiff, who commended the FBI Director for serving with "great professionalism and integrity".
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