The inquiry into historical child abuse in the UK will continue its work for now - despite the resignation of the second person appointed to chair it.
Commons leader William Hague told the BBC that the inquiry panel would "go on with its work" while the government searched for another chairman.
Fiona Woolf quit amid concerns about her links to establishment figures.
Labour's Yvette Cooper said the new chair must have the confidence of victims' groups.
Lib Dem peer Lord Carlile told Sky News it should not be a parliamentarian, and the government should look "north of Watford" for someone with experience dealing with child abuse and child protection who was not part of the "Westminster Village".
Home Secretary Theresa May will make a statement to Parliament on Monday about how the inquiry will proceed following Mrs Woolf's resignation on Friday.
Mr Hague told BBC One's Andrew Marr Show: "We are determined that this inquiry will happen and will be able to do its work. There are so many deeply disturbing things for it to look into.
"Clearly some terrible things have happened over many years. We have got to find out the truth about that. So we have to somehow maintain and restore the momentum of this work."
The inquiry will look at whether public bodies and other institutions did enough to protect children from sexual abuse, from 1970 to the present day.
It follows claims over many years about paedophiles in powerful places and alleged establishment attempts to cover up their actions.
It was announced in July, but the first person appointed to chair it, Baroness Butler-Sloss, stepped down shortly afterwards when concerns were raised about the fact that her late brother was attorney general during the 1980s.
On Friday her replacement, Mrs Woolf, quit after weeks of reports about her social connections with Leon Brittan, who was home secretary in 1984 when ministers were handed a dossier on alleged high-profile paedophiles.
Shadow home secretary Yvette Cooper told Sky News: "The most important thing is that we can rebuild the credibility of this inquiry. We have had four months of chaos and confusion."
She said the inquiry must "get going" and must have the confidence of abuse survivors: "That is something the home secretary has failed to do."
Meanwhile, Home Secretary Theresa May is "considering the findings" of the Wanless review, the BBC has learned.
In July, NSPCC chief executive Peter Wanless was tasked with examining a 2013 Home Office report about how papers containing claims of child sex abuse by politicians were handled.
That report found there were no records of specific claims of abuse by prominent figures. It had been triggered by claims that allegations made by the late MP Geoffrey Dickens were ignored.
However, it was discovered that 114 files could no longer be located.
Mr Wanless was also tasked with looking at how the police and prosecution authorities handled any material that was handed to them at the time.