The decision on the FBI director’s future, which was first reported by CNBC, was confirmed by White House press secretary Jen Psaki, who had previously declined to answer whether the president continued to have confidence in Mr Wray on her first day in the role.
Seeking to clarify her remarks on Thursday, Ms Psaki wrote on Twitter that the president did in fact have confidence in Mr Wray, and wanted him to continue in his position.
“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,” said Ms Psaki.
A source told CNN beforehand that the press secretary was simply unaware that Mr Biden had reached out to Mr Wray, and was expected to say at Thursday’s White House press conference that the new administration wanted to keep the FBI director in post.
"I have not spoken within him about specifically FBI Director Wray in recent days," Ms Psaki had said, "but I'll circle back if there's more to convey."
Mr Wray, who has appointed in August 2017, will be expected to serve the remaining six years of his tenure at the FBI, whose directors are limited to 10-year terms.
Although he was appointed by the former president, the FBI director became a frequent target of Mr Trump over his refusal to back false claims of voter fraud in November’s election.
Speaking about possible Russian interference in the presidential race, Mr Wray told lawmakers last September that “what concerns me the most is the steady drumbeat of misinformation."
He added: "I worry that people will take on a feeling of futility because of all the noise and confusion that is generated, and that’s a very hard problem to combat”.
Mr Trump, who similarly pushed false claims of election fraud, was also said to be unhappy with Mr Wray for not announcing investigations into his political opponents, including the Mr Biden’s son, Hunter Biden, before the election, but had stopped short of firing him.
Mr Wray is currently overseeing the FBI’s response to the 6 January attack on the US Capitol by Mr Trump’s supporters, who falsely alleged the election was “rigged”. Five people, including a Capitol Police officer, lost their lives in the riot.
Already, the FBI has arrested over a 100 people in connection to the attack, and are believed to be investigating “hundreds more”.