Dame Lowell Goddard resigned as chair of the national child sexual abuse inquiry days after the Home Office was notified of concerns about her "professionalism and competence", it has emerged.
Officials said they were made aware of concerns on July 26, before the New Zealand high court judge became the third person to step down as head of the inquiry on August 4.
A Home Office spokeswoman said: "On July 29 the Home Office was made aware of concerns about the professionalism and competence of Justice Goddard.
"The permanent secretary advised the inquiry that as they were independent, they should raise this directly with the chair. It is understood that they did this.
"No formal complaint was made to the Home Office. Justice Goddard resigned on August 4."
The Times reported that Dame Lowell allegedly made racist remarks, saying Britain had so many paedophiles because it had so many Asian men.
Whitehall officials close to Theresa May are also alleged to have covered up the claims of Dame Lowell's misconduct and racist comments.
The high court judge denied the allegations, saying they were "malicious" and part of a "vicious campaign".
"I confirm my absolute rejection of this attack," Dame Lowell said. "I am confident that in New Zealand, my known reputation from my work over many years will provide its own refutation of these falsities."
Shadow home secretary Diane Abbott said Theresa May, who was home secretary at the time of Dame Lowell's appointment, and the Home Office itself, had "serious questions to answer".
"This inquiry has a lot of ground to cover, but it is already on its fourth chair and now there are suggestions that Home Office officials turned a blind eye to allegations of impropriety." she said.
Ms Abbott added: "How can the victims expect this inquiry to uncover child abuse when it has faced multiple setbacks of its own?"
Downing Street declined to comment on whether Mrs May was informed about concerns allegedly reported to her officials during her time as home secretary.
The Prime Minister's spokeswoman said: "With regard to the allegations that have been reported today, the Home Office has made it very clear that they don't regard it as appropriate to comment on individual staffing matters of this sort. I have nothing to add to that."