James Brokenshire defended the appointment of Lady Butler-Sloss, who has faced claims she refused to go public about a bishop implicated in a scandal. She told a victim of alleged abuse she did not want to include the allegations in a review of how the Church of England dealt with two paedophile priests because she "cared about the Church", it was claimed.
It put fresh pressure on the former High Court judge, who has faced calls to step down after reports that her brother, Sir Michael Havers, tried to prevent ex-MP Geoffrey Dickens airing claims about a diplomat in Parliament in the 1980s.
Lady Butler-Sloss insisted that she has "never" put the reputation of an institution ahead of justice for victims.
Mr Brokenshire said yesterday: "I think that Baroness Butler-Sloss'integrity shines through."
Asked if there could be co-chairmen with equal powers, he told Murnaghan on Sky News: "I think it's this precise detail that we are working on at this stage because it is important that we do draw on the right experts."
Shadow Home Secretary Yvette Cooper repeatedly dodged questions over whether Labour backed Lady Butler-Sloss as the right person to chair the inquiry.
She told Murnaghan: "I think she is an extremely experienced person who will be very good to do this job but she also needs the right people around her, she needs the Home Office to take action to make sure they address all of these concerns.
"If they can't they will need to make changes and rethink the whole thing but I think the ball should be in the Home Office's court now to set this up in the right way."
The Archbishop of Canterbury has admitted that the inquiry is likely to turn up fresh claims about the Church of England.
The Most Rev Justin Welby said it was something he dealt with daily, and it was becoming clearer that "for many, many years things were not dealt with as they should have been dealt with".