If Oxfam doesn't fully cooperate "then I can not work with them anymore as an aid delivery partner", she said.
Oxfam workers were accused of paying Haitian natural disaster survivors for sex during relief efforts.
The Charity Commission said on Saturday that it had written to Oxfam "as a matter of urgency" to request further information.
"If the moral leadership at the top of the organization isn't there, then we can't have you as a partner", she said.
In an emailed statement to dpa on Sunday, Oxfam said it would "strive to clarify as soon as possible whether the [Chad] allegations were known to us and what measures were taken".
Britain will cut off aid funding from any organisation that does not comply with a new review into charities work overseas, aid minister Penny Mordaunt said on Sunday, describing reports of sexual exploitation in the sector as "utterly despicable".
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The charity confirmed it had dismissed four people and allowed three others to resign in the case after an investigation uncovered offences including sexual misconduct, bullying, intimidation and failure to protect staff.
"I had quotes from the United Nations report", she said. "We were not told about the nature of these events".
"I have so much respect for Oxfam, they do great work, but this is a sector wide problem", the former staffer told the Observer.
Responding to a report in The Times newspaper, Oxfam admitted that the behaviour of some of its staff had been "totally unacceptable".
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.
The British Red Cross says it received a small number of harassment reports involving language or behaviour and that all the cases involved actions in the U.K. It said "even a small number of incidents is too many".
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The comments by Mattis came on the heel of deadly US-led coalition air strikes which killed some 100 pro-Syrian government forces. It also said it was aware only of 25 Syrian militia members having been wounded in the United States strikes.
'We are shocked and dismayed about the latest revelations from Chad.
He 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.
Goldring apologised yesterday and said he was 'deeply ashamed of Oxfam's behaviour [in Haiti]'.
Ms Thomson said she was working closely with chief executive Mark Goldring to make improvements.
Oxfam's chairwoman of United Kingdom trustees, Caroline Thomson, said it was working to "address the underlying cultural issues that allowed this behaviour to happen".
She added: "what is so disturbing about Oxfam is that when this was reported to them, they completely failed to do the right thing".
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Oxfam said it now had a dedicated safeguarding team, a confidential whistleblowing hotline and safeguarding contact point within countries, and a code of conduct that stipulated: "I will also not exchange money, offers of employment, employment, goods or services for sex or sexual favours".