In a further warning to the charity, she said: "If they do not hand over all the information that they have from their investigation and subsequently to the relevant authorities, including the Charity Commission and prosecuting authorities, then I can not work with them any more as an aid delivery partner".
"If they do not hand over all the information they have from their investigation subsequently to the relevant authorities including the Charity Commission and prosecuting authorities, then I can not work with them any more".
She confirmed the charity would meet with the Department for International Development (DFID) on Monday and the Charity Commission, which regulates the sector, later this week.
If the moral leadership at the top of the organisation is not there then we can not have you as a partner.
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.
It is a "complete betrayal of both the people Oxfam were there to help and also the people that sent them there to do that job", Britain's global development secretary, Penny Mordaunt, told BBC News, which noted that the nonprofit received $44 million in government funds past year.
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.
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". "We were not told about the nature of these events".
Reuters could not independently verify the allegations contained in The Times report and was unable to reach any of the Oxfam staff who worked in Haiti.
More reports of misconduct have emerged since the original report in the Times.
Oxfam said it could not corroborate the latest claims but it said it was "shocked and dismayed" at what it called the unacceptable behaviour by a small number of people.
Oxfam said it was "shocked and dismayed" by the new Chad claims.
The regulator said an Oxfam report on the investigation stated there had been no allegations of abuse of beneficiaries and made no mention of any potential sexual crimes involving minors.
Goldring apologised yesterday and said he was 'deeply ashamed of Oxfam's behaviour [in Haiti]'.
Oxfam, one of the world's most prominent relief agencies, could lose its funding from the British government over reports that its workers exploited survivors of a massive quake in Haiti, and possibly other disasters, for sex.
The charity said it launched an immediate investigation in 2011 which found a "culture of impunity" among some staff but has denied trying to cover up the scandal. The charity employs 5,000 staff and has a further 23,000 volunteers.
Ms Mordaunt announced she would meet the charity on Monday to discuss the case, and said: 'If the moral leadership at the top of the organisation is not there then we cannot have you as a partner'.
Marr said: "That was a lie, wasn't it?" However, the minister said Oxfam did "absolutely the wrong thing" by not reporting the detail of the incidents to the government.