Dame Lowell Goddard resigned as head of the national child sexual abuse inquiry days after the Home Office was made aware of concerns about her "professionalism and competence".
The department said it was told of the concerns on July 29 before Dame Lowell resigned on August 4.
Officials were unable to say whether similar misgivings were raised before that date, but questions have been asked about how much Theresa May was told during her time as home secretary.
Mrs May left the Home Office to become Prime Minister on July 13, appointing Amber Rudd as Home Secretary.
On September 7, Ms Rudd told the Commons Home Affairs Committee she believed the New Zealander had quit because she was "a long way from home", "found it too much", and was "too lonely".
"That's all the information I have about why she decided to go," the Home Secretary added.
But her department has now revealed that worries were raised about Dame Lowell, who has denied allegations she used racist language while chair, before that date.
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."
Dame Lowell has described allegations made in The Times as "falsities", "malicious" and part of a "vicious campaign".
The newspaper reported a number of claims made by what it said were "well-placed figures" at the inquiry's headquarters about her alleged conduct, including that she said Britain had so many paedophiles because it has so many Asian men.
The New Zealand high court judge said she had consulted lawyers in London about the allegations.
She added: "I confirm my absolute rejection of this attack. I am confident that in New Zealand my known reputation from my work over many years will provide its own refutation of these falsities."
Earlier, 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 official 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."
Shadow home secretary Diane Abbott said: "Theresa May and the Home Office have 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.
"How can the victims expect this inquiry to uncover child abuse when it has faced multiple setbacks of its own?
"After years of waiting for justice they deserve better. It is crucial that this inquiry gets on with its vital task."
The beleaguered inquiry has been plagued by problems since it was launched in 2014.
When she resigned, Dame Lowell called for the probe to be overhauled, saying "there is an inherent problem in the sheer scale and size".
Professor Alexis Jay replaced her as chairwoman.
The probe - described as the most ambitious public inquiry ever in England and Wales - was earmarked to take five years, but there have been suggestions it could run for as long as a decade.
Last month the inquiry's senior lawyer Ben Emmerson QC resigned after being suspended amid reports he was about to step down.
The departure was announced just hours after it was revealed his junior colleague Elizabeth Prochaska had also left her role.
In the wake of the resignations, Prof Jay refuted suggestions Mr Emmerson had quit because of a difference of opinion with her about the inquiry's future.
Shortly before Dame Lowell quit, The Times revealed that she had spent more than 70 days working abroad or on holiday during her time in charge.
The inquiry's financial report for 2015/16 included details of spending amounting to more than half a million pounds in relation to Dame Lowell's terms.
The inquiry incurred costs of £67,319 during the last financial year on travel included in the New Zealand high court judge's terms of appointment.
"This included travel to and from New Zealand for her and her family," the report said.