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.
"Our approach to this matter would have been different had the full details that have been reported been disclosed to us at the time", the commission said.
She admitted she was considering whether the organisation should receive any more funding from the Department for International Development - which gave it £32m in the last financial year.
If the moral leadership at the top of the organisation is not there then we can not have you as a partner.
The charity said allegations that under-age girls may have been involved were not proven.
The worldwide development secretary has said the government will end funding to Oxfam unless the charity shows "moral leadership" and hands over all its information on its aid workers' apparent use of prostitutes in Haiti.
Four members of Oxfam staff were dismissed and three, including the country director, resigned before the end of the 2011 investigation.
She will also seek to confirm they have referred all concerns about specific cases and individuals to the relevant authorities. "We were not told about the nature of these events".
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".
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The government's hardening stance follows reports in The Times newspaper that young sex workers were hired by Oxfam's senior staff in Haiti after the 2010 natural disaster which devastated the island and left up to 300,000 people dead.
Mordaunt told BBC that she would meet with Oxfam officials on Monday, but she sounded unimpressed by the nonprofit's promises to reform.
It said one of the instances was "a case of failings in adequate safeguarding", which was reported to the Charity Commission.
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.
Oxfam chief executive Mark Goldring apologised on Saturday, saying he was deeply ashamed of Oxfam's behaviour.
There had been other incidents since 2011, he said, but "nothing on the scale of this severity".
And it will extend an existing review into bad behaviour and the charity's culture to include looking at how people are hired and managing of staff in challenging environments. Asked if that was a lie, Mordaunt said: "Well, quite".
She added that Oxfam had done "absolutely the wrong thing" by failing to inform authorities about the full details of the allegations.
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".