Ms Mordaunt's announcement comes as the Observer reports that Oxfam workers allegedly used prostitutes in Chad in 2006.
Asked by Marr if she thought Oxfam had failed in its "moral leadership", Ms Mordaunt replied: "Yes, I do".
At the time, the charity only referred to it as "serious misconduct".
Oxfam received almost £32m from the government in the last financial year.
"I think we should have been open that there was sexual misconduct and that involved the use of prostitutes", he said.
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.
The staff had been in as part of the relief effort following the devastating magnitude 7.0 quake that killed more than 200,000 people there in 2010.
Mr Van Hauwermeiren went on to work elsewhere in the sector.
"Moreover we received positive references from former Oxfam staff-in their individual capacities-who worked with him", including from a human resources staffer, a spokesman said.
"The horrific behaviour by some members of Oxfam staff in Haiti in 2011 is an example of a wider issue on which DfID (Department for International Development) is already taking action, both at home and with the international community via the United Nations".
"There are some actions I'm looking for them taking now". It is not clear whether anyone from DFID made any attempt to investigate what the "nature of the allegations" was.
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The UK now spends £13bn on aid each year and there have always been calls from some Conservative MPs for cuts to this budget.
Britain will cut off aid funding from any organisation that does not comply with a new review into charities work overseas, the country's aid minister has said.
Labour, the Liberal Democrats, SNP, Greens and Plaid Cymru also agree that figure should remain.
Oxfam Chief Executive Mark Goldring said Saturday it receives less than 10 percent of its funding from DFID and hoped to continue working with the department while rebuilding trust with the public.
Ms Mordaunt said she was writing to all British charities that receive United Kingdom aid to insist they detail the steps they are taking to ensure safeguarding policies are fully in place.
A DfID spokesman said: "We often work with organisations in chaotic and hard circumstances".
"We stand firmly against the exploitation and abuse of women and girls".
Britain's International Development Secretary Penny Mordaunt warned today Oxfam must hand over to authorities any information it has collected on a "shocking" staff prostitution scandal in Haiti or face repercussions.
Andrew Mitchell, who was worldwide development secretary in 2011, told 's Newsnight it was a "shudderingly very bad tale" that was "terrible on every single level".
There had been other incidents since 2011, he said, but "nothing on the scale of this severity".