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.
An investigation by The Times alleges the charity covered up sexual misconduct by aid workers in Haiti. In a sign of widening fallout, the Sunday Times reported more than 120 workers for Britain's leading charities were accused of sexual abuse in the past year.
"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.
Oxfam's chief executive has denied there was any cover-up after it was revealed some of its aid workers used prostitutes in Haiti in 2011.
Former Oxfam staff in Chad told the paper that "women believed to be prostitutes were repeatedly invited to the Oxfam team house there", and a senior staff member was sacked for his behaviour in 2006.
Responding to Mordaunt's comments, Oxfam's Chair of Trustees Caroline Thomson said she shared the "anger and shame that behavior like that highlighted in Haiti in 2011 happened in our organization".More news: Asma Jahangir: Her life in pictures
"Unfortunately, there is nothing we can do to stop individuals falsifying references, getting others that were dismissed to act as referees and claiming it was a reference from Oxfam", a spokeswoman added.
Mordaunt, speaking to the BBC, said she would meet Oxfam representatives on Monday.
"People knew in DfID, I raised this directly with my department at the time", she said. They initially said they were investigating misconduct, and when they concluded that report they did not tell us the nature of these events.
The charity had shown an "absolute absence of leadership", she said.
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 has written to all organisations funded by her department, telling them to report any safeguarding issues.More news: Is Trump More Popular Than Obama?
She added that Oxfam had done "absolutely the wrong thing" by failing to inform authorities about the full details of the allegations.
The charity also said it had yet to find evidence proving allegations that underage girls were involved.
Penny Mordaunt said it was "despicable" that sexual exploitation and abuse still existed in the aid sector.
Oxfam has denied allegations that it tried to hide that some of its staff paid prostitutes in the aftermath of the natural disaster.
Oxfam's boss say he is "deeply ashamed" over accusations its staff used prostitutes in Haiti in the aftermath of the 2010 natural disaster.
It announced on Sunday that one investigation led to the dismissal of a staff member, while the other case resulted in disciplinary action (not dismissal).More news: Many in his party are angry he wanted the foreign minister position