Some of Oxfam's staff allegedly hired prostitutes while in Haiti trying to help the country recover from the 2010 quake.
Oxfam is facing mounting criticism over its handling of sex allegations, but has denied trying to cover up the use of prostitutes by workers in Haiti in 2011.
The Times of London on Friday published a report with details of a leaked internal investigation of the alleged payment for sex with young women, possibly including under-age girls, by Oxfam staff in Haiti.
"What I'm apologising for is that nine Oxfam staff behaved in a way that was totally unacceptable and contrary to our values, and that led much more responsible staff to make decisions which are now seen by some as being marginal or inappropriate".
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Oxfam has been at the centre of a firestorm of controversy after it was revealed that Oxfam staff had paid for sex whilst working in Haiti.
Estimates vary but around 220,000 people were killed in the Haiti disaster and millions left homeless in a country where more than half of the population live in poverty.
Ms Mordaunt revealed the charity had "categorically" stated to the Department for International Development (DfID) that no harm was done and beneficiaries were not involved, which she said was a lie.
"With regard to Oxfam and any other organisation that has safeguarding issues, we expect them to co-operate fully with such authorities, and we will cease to fund any organisation that does not".
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Mr Goldring added that a safeguarding team had been set up to improve the quality of reporting investigations, as well as a "whistle-blowing line". She added: "If the moral leadership at the top of the organisation isn't there, then we cannot have you as a partner".
"I want to protect and preserve that".
Caroline Thompson, who chairs Oxfam Great Britain's board of trustees, said charities that work in "fragile and unstable environments can become targets for abusers", but that the organization is committed to fixing the problems it faces.
The United Kingdom's Department for International Development sharply criticized the charity for its lack of transparency as questions swirled about how much detail Oxfam provided when it first reported the allegations.
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Global development secretary Penny Mordaunt said it was "despicable" that sexual exploitation and abuse existed in the aid sector and threatened to cut funding to charities if they fail to comply with authorities over safeguarding issues.