The talent show judge was heard making offensive and sexually explicit comments, according to a transcript of a recording that was leaked, the Guardian said.
The comments "were never intended to be disseminated," he has apologised.
Producers of the show claimed to have discussed his "future professional conduct" with him.
Since 2012, the comedian and author has made appearances on the ITV show.
The television personality stated in a statement: "I want to apologise to the individuals I disparaged during breaks in the 2020 season of Britain's Got Talent filming.
"Like the majority of chats with friends, these were private and weren't meant to be shared. However, I apologise."
The statements were overheard by microphones when the judging panel was in conversation and the London Palladium was taping an audition show, according to the Guardian.
One allegedly targeted a more experienced performer who had made fun of Walliams while laughing with the judges.
In the second incident, a woman left the stage shortly after Walliams allegedly called her a "somewhat dull female you meet in the pub" who believes you want to have sex with her.
ITV stated in a statement: "We have spoken with the creators of Britain's Got Talent, and we do not support the language mentioned in these accusations.
We have rules and guidelines in place for all of our manufacturing partners, and our duty of care to everyone who participates in any of our programmes is always of the utmost importance.
The show's producer, Thames TV, said it considered Walliams' comments to be private but found his language to be "unacceptable."
"Even though it was personal, all concerned have been spoken to and reminded of their obligations and the show's standards as to future professional conduct," they continued.
Britain's Got Talent's co-producers, Simon Cowell and Syco Entertainment, claimed they were "unaware" of the allegedly inappropriate chat until contacted by the newspaper. They emphasised that "Britain's Got Talent is a family show and we do not condone the use of any such language."
There is no evidence that Cowell or any other judge said anything along those lines.
Walliams, known for his on-screen relationship with Cowell on the programme, won the National Television Awards' top judge honours in 2015, 2018 and 2019.
As the actor and co-creator of the popular BBC sketch show Little Britain in the 2000s, he first gained notoriety. Since then, he has enjoyed success as a best-selling children's author.
He and his Little Britain co-star Matt Lucas did, however, issue an apology for the use of black face in the programme in 2020, and last year, a narrative about a Chinese child was cut from one of his books as a result of complaints that it included "damaging stereotypes."