The charity commission demanded further information from Oxfam on Saturday, saying it had "made no mention of any potential sexual crimes involving minors", when it first reported the investigation in 2011.
Oxfam workers were accused of paying Haitian natural disaster survivors for sex during relief efforts.
"Our approach to this matter would have been different had the full details that have been reported been disclosed to us", the commission said. The charity had shown an "absolute absence of leadership", she said.
Mordaunt said Oxfam had told her department "categorically no" when it had asked if any beneficiaries of aid had been involved in or affected by the misconduct.
The worldwide 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.
British charity Oxfam says it will strengthen its internal safeguards in response to allegations staff members working in Haiti following the devastating 2010 quake engaged in sexual misconduct.
And there was also nothing to stop them from getting former or current staff to provide a reference "in a personal capacity", she said.
They include a pledge to work with other charities to overcome "the legal difficulties which have so far prevented us from sharing intelligence" about staff accused of misconduct.
Former Oxfam employees in Chad claimed staff held sex parties with prostitutes.
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"I'm deeply ashamed [of] Oxfam's behaviour and everybody, the 25,000 staff and volunteers are compromised by this", CEO Mark Goldring said.
Responding to a report in The Times newspaper, Oxfam admitted that the behaviour of some of its staff had been "totally unacceptable". The British Red Cross told the paper there had been a "small number of cases of harassment reported in the UK".
The charity is under growing pressure after an investigation by The Times found young sex workers were hired by senior staff in Haiti after the 2010 quake which devastated the island and left up to 300,000 people dead.
'We are shocked and dismayed about the latest revelations from Chad.
There had been other incidents since 2011, he said, but "nothing on the scale of this severity".
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.
And it will extend an existing review into bad behaviour and the charity's culture to include looking at how people are hired and managing of staff in challenging environments.
Marr said: "That was a lie, wasn't it?"
Ms Mordaunt said it did not matter how good the safeguarding practices were in an organisation if they did not "have the moral leadership to do the right thing".