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.
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".
The Sunday Times reported that there had been more than 120 cases of sexual harassment or abuse recorded at some of Britain's leading charities in the past year alone, with the highest number at Oxfam, who recorded 87 incidents last year.
United Kingdom officials have said that Oxfam needs to hand over all its information on the issue in order to not lose funding.
The scandal deepened on Sunday when The Observer newspaper claimed sex workers were also used during a 2011 relief mission in Chad.
The former Secretary of State said that "the reason why Oxfam has landed in this position is because they have not been fully open and transparent about what happened".
However, Mordaunt said not disclosing the full picture was "a scandal" and today's meeting was a chance "to see if they are displaying the moral leadership that I think they need to now".
The Charity Commission said on Saturday that it had written to Oxfam "as a matter of urgency" to request further information.
Mordaunt, speaking to the BBC, said she would meet Oxfam representatives on Monday.
The charity had shown an "absolute absence of leadership", she said.
Oxfam said it publicly announced an investigation into the allegations when they surfaced and kept the Charity Commission informed.
She said that as a direct result of the Times story, staff members had raised concerns about how employees in Haiti were vetted and recruited.
"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".
"It is utterly despicable that sexual exploitation and abuse continues to exist in the aid sector", Ms Mordaunt said.
In a statement, Oxfam denied providing positive references for those implicated, and said they were likely provided on an individual capacity.
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".
The Times of London, which first exposed the scandal, has reported that several of the aid workers dismissed by Oxfam for inappropriate behavior found work with other aid agencies.