The charity should immediately hand over its entire 2011 investigation into the sexual misconduct to the appropriate prosecuting authorities and the Charity Commission, she said.
Oxfam workers were accused of paying Haitian quake survivors for sex during relief efforts.
Caroline Thomson, the chair of Oxfam Great Britain's board of trustees, says charities that work in "fragile and unstable environments can become targets for abusers".
Ms Mordaunt said it was her "absolute priority" to keep the world's most vulnerable people safe from harm.
"If the moral leadership at the top of the organization isn't there, then we can't have you as a partner", she said.
Oxfam said it had already taken measures to prevent sexual abuse and misconduct, including the launch of a hotline to report allegations.
International Development Secretary Penny Mordaunt said the charity completely failed to do the right thing after it was reported aid workers hosted sex parties with prostitutes on a 2010 mission to Haiti.
In addition to the country director, six other workers left the charity after its internal investigation: Two resigned and four were fired for offenses such as "use of prostitutes on Oxfam property" and possession of pornography, the Times reported.
And there was also nothing to stop them from getting former or current staff to provide a reference "in a personal capacity", she said.
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'We also want to satisfy ourselves that we do now have a culture of openness and transparency and that we fully learn the lessons of events in 2011'.
The majority of Oxfam's 230 staff members working in Haiti at the time are not accused of doing anything improper, but a small group of male aid workers living in Delmas, near Port-au-Prince, allegedly turned a rented guesthouse into what a source told the Times the men called "the whorehouse".
Staff who worked for the charity in Chad alleged in the Observer that women believed to be prostitutes were repeatedly invited to the Oxfam accommodation there as well.
But as well as being a public relations disaster for Oxfam, the scandal could cost them $50 million in government funding.
The Sunday Times reported that there had been more than 120 cases of sexual harassment or abuse recorded at some of Britain's leading charities in the past year alone, with the highest number at Oxfam, who recorded 87 incidents last year.
"Unfortunately, there is nothing we can do to stop individuals falsifying references, getting others that were dismissed to act as referees and claiming it was a reference from Oxfam", a spokeswoman added.
Everybody - the 25,000 staff and volunteers - are compromised by this, the hundreds of thousands of people who support Oxfam every month are compromised by this, and to everybody I apologise, he said.
Marr said: "That was a lie, wasn't it?"
However, Mordaunt said not disclosing the full picture was "a scandal" and Monday's meeting was a chance "to see if they are displaying the moral leadership that I think they need to now".