David Cameron remains confident that Baroness Butler-Sloss is the right person to lead the child abuse inquiry, his official spokesman said, adding: "She commands the very highest respect for her professional expertise and integrity.
"His view is that she does command widespread respect and confidence, and rightly so".
The Baroness says she did not consider the "difficulties" caused by her background and family connections to the child sex abuse inquiry.
Questions have been raised of former High Court judge Baroness Butler-Sloss since her appointment last week.
22 police officers are now assigned to Operation Fernbridge - the probe into claims of a Westminster cover-up of sex child abuse.