Mordaunt said she was writing to all charities that receive state aid demanding they step up efforts to tackle sexual misconduct among staff or face funding cut-offs.
In a further warning, 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".
"With regard to Oxfam and any other organisation that has safeguarding issues, we expect them to cooperate fully with such authorities, and we will cease to fund any organisation that does not", she said in a statement.
Christian Aid's comments come after Oxfam has been accused of covering up the use of prostitutes by aid workers in Haiti in 2011.
The former International Development secretary Priti Patel told the BBC: 'There are no databases of these predatory paedophiles that exist and we need them ... to stop this disgusting and corrosive culture of the revolving door in aid agencies'.
Ms Mordaunt said the charity had done absolutely the wrong thing by failing to tell the Charity Commission and prosecuting authorities the full details of the allegations.
Oxfam will examine new complaints from staff members about how the aid workers involved in 2010 were recruited and vetted.
Ms Mordaunt said she would write to British charities working overseas demanding they declare any problems relating to the duty they have to protect their staff and the people they work with from harm and abuse - so-called "safeguarding".
Drake goes on charity spending spree in Miami
Drake also gave an impromptu concert at the University of Miami , where he awarded a $50,000 scholarship to a lucky student. More good deeds included buying a van and ice cream for Overtown Youth Center, where it was clearly very much appreciated.
"If they do not hand over all the information they have from their investigations to the relevant authorities.then I can not work with them".
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".
"Moreover we received positive references from former Oxfam staff who worked with him, among them a (former) HR person", a spokesman added.
She added that sexual abuse in the charity sector as "utterly despicable", and vowed to meet the charity commission to discus what more could be done to fight it.
He said that it was very important to remember that "there are thousands of people working for Oxfam in some of the most hard places. and we must not forget that Oxfam is one of Britain's most brilliant charities".
To date, four employees were fired from their posts and another three resigned before the investigation was complete.
She has written to all organisations funded by her department, telling them to report any safeguarding issues.
Oxfam has denied that they took part in any coverup thought according to reports they did not let the Haitian government what was happening which meant they were unable to take legal action against the employees involved.