The global development secretary has said the government will end funding to Oxfam unless the charity shows "moral leadership" and hands over all its information on its aid workers' apparent use of prostitutes in Haiti.
"Our approach to this matter would have been different had the full details that have been reported been disclosed to us at the time", the Charity Commission said in a statement.
Ms Mordaunt said it was her "absolute priority" to keep the world's most vulnerable people safe from harm.
Late on Friday, the Department for International Development (DFID) also said it was reviewing its relationship with the UK-based charity, to which it gave almost £32 million (36 million euros/$44 million) previous year.
The scandal deepened on Sunday when The Observer newspaper claimed sex workers were also used during a 2011 relief mission in Chad.
The British government, meanwhile, has threatened to cut off funding to Oxfam, or any other aid organization that doesn't cooperate with the government's new effort to crack down on such abuses, according Mordaunt, who expects to meet with Oxfam officials on Monday.
She said the reports were "a complete betrayal of the people Oxfam were there to help and also the people that sent them there to do that job".
"If they do not hand over all the information that they have from their investigation. then I can not work with them any more as an aid delivery partner - and any other organisation in those circumstances", she told the BBC.
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The chief executive said: "With hindsight, I would much prefer that we had talked about sexual misconduct".
"But I don't think it was in anyone's best interest to be describing the details of the behaviour in a way that was actually going to draw extreme attention to it".
British charity Oxfam says it will strengthen its internal safeguards in response to allegations staff members working in Haiti following the devastating 2010 natural disaster engaged in sexual misconduct.
Goldring apologised yesterday and said he was 'deeply ashamed of Oxfam's behaviour [in Haiti]'.
The scale of abuse in the charity sector was revealed last week when it emerged that shamed Oxfam Haiti director Roland van Hauwermeiren, 68, left the charity with six other men after getting caught using prostitutes, downloading "pornographic and illegal material". "We were not told about the nature of these events".
"Moreover, we received positive references from former Oxfam staff - in their individual capacities - who worked with him", including from a human resources staff member, a spokesman said.
MPs have warned about "predatory paedophiles" following sexual assault allegations against more than 120 workers for British leading charities.
"Sexual abuse is a blight on society and Oxfam is not immune", Thomson said.