It said Oxfam's leaders had "showed a lack of judgement" in their handling of the matter and their level of openness with the government and Charity Commission.
In a sign of widening fallout from the scandal, the Sunday Times reported more than 120 workers for Britain's leading charities were accused of sexual abuse in the past year, "fuelling fears paedophiles are targeting overseas aid organisations".
Numbers collected by four of Britain's leading overseas aid charities, seen by The Sunday Times, revealed that 125 allegations of sex abuse were made previous year alone.
"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", Mordaunt said in a statement.
He is expected to insist that Oxfam did not inform ministers of the.
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".
Meanwhile an Oxfam spokeswoman has said the charity would not have provided a positive reference for any of those who were dismissed or resigned.
Speaking about the allegations, she said: "I think it's a complete betrayal of both the people Oxfam were there to help and also the people that sent them there to do that job".
Oxfam Chief Executive Mark Goldring said Saturday it receives less than 10 percent of its funding from DFID and hoped to continue working with the department while rebuilding trust with the public.
"We want to see Oxfam provide all the evidence they hold of the events to the Charity Commission for a full and urgent investigation of these very serious allegations".
Penny Mordaunt said it was "despicable" that sexual exploitation and abuse still existed in the aid sector.
Penny Mordaunt hit out at Oxfam officials who had used prostitutes while working in Haiti after the 2010 natural disaster, dubbing their behaviour "despicable".
The Times of London on Friday published a report with details of a leaked internal investigation of the alleged payment for sex with young women, possibly including under-age girls, by Oxfam staff in Haiti.
She said it had made big changes since the original incident but that today I commit that we will improve further.
"They did tell the Charity Commission there was sexually inappropriate behaviour, bullying and harassment of employees, but they did not report that to us".
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.