International Development Secretary Penny Mordaunt said it was "shocking" that some Oxfam staff had been able to resign after the Haiti sex allegations surfaced.
She told BBC1's The Andrew Marr Show: "I think it's shocking and it doesn't matter how good the safeguarding practices are in an organisation, if that organisation does not have the moral leadership to do the right thing, and where in particular they have evidence of criminal activity to pass that information to the relevant authorities including prosecuting authorities, that's an absolute absence of leadership."
Marr asked: "So you feel that Oxfam failed in its moral leadership?"
She replied: "Yes, I do."
Ms Mordaunt (pictured) said she would meet Oxfam on Monday to discuss the scandal.
She told the programme: "I am affording them the opportunity to tell me in person what they did after these events and I'm going to be looking to see if they are displaying the moral leadership that I think they need to now.
"We are talking about a historic case but it is in some respects still live, they still have information they should be giving to the authorities."
Ms Mordaunt said the Department for International Development was not told about the events at the time.
She said: "They initially said that they were investigating misconduct and when they concluded that report they did not tell us the nature of these events.
"They did tell the Charity Commission that there was sexual inappropriate behaviour, bullying and harassment of employees but they did not report that to us."
She added that Oxfam also reassured the department that no harm was done and there was no involvement of any beneficiaries.
Marr said: "That was a lie, wasn't it?"
Ms Mordaunt replied: "Well, quite."
She said she did not know what Oxfam's motivation was for handling the investigation as it did, and warned that its relationship with the Government was at risk.
"If the moral leadership at the top of the organisation is not there then we can not have you as a partner," she said.
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.
She added: "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 cannot work with them any more as an aid delivery partner."
Former International Development Secretary Priti Patel told BBC Radio 5 Live's Pienaar's Politics she was aware of abuse involving aid workers in disaster zones.
She said did her own research when she headed the department, speaking to people within the sector who have been whistle blowers, and looked at "well-documented" evidence.
She told the programme: "People knew in DfID, I raised this directly with my department at the time.
"I had quotes from the United Nations reports on the number of people.
"I think even the Secretary General last year said there were 120 cases involving something like over 300 people, and that was just the tip of the iceberg."
Ms Patel said she was not aware of allegations specifically in Oxfam, but that there were documented cases in other NGOs.
She told the programme: "There has been in my view, not just a cover-up with Oxfam, there is a denial, a culture of denial in the aid sector about the exploitation and sexual abuse that has taken place historically for decades."
She added: "My former department did not raise this issue with me, I raised it with them through my own investigations and my own research and I challenged them."
Caroline Thomson, Oxfam's chairwoman of trustees in the UK, said the charity was "ashamed" of what had happened in Haiti, adding that it prides itself on "being a transparent organisation".
"It is clear that such behaviour is completely outside our values and should never be tolerated," she said.
Ms Thomson said she was working closely with chief executive Mark Goldring to make improvements.
"We will continue to address the underlying cultural issues that allowed this behaviour to happen," she said.
"We also want to satisfy ourselves that we do now have a culture of openness and transparency and that we fully learn the lessons of events in 2011."
Since the publication of The Times' investigation, Ms Thomson said Oxfam staff have come forward with concerns about the recruitment and vetting of workers involved in the scandal.
"We will examine these in more detail to ensure we further strengthen the improved safeguarding, recruitment, vetting and staff management procedures that were put in place after 2011," she said.
Announcing measures to improve safeguarding within Oxfam, Ms Thomson said: "It is not sufficient to be appalled by the behaviour of our former staff - we must and will learn from it and use it as a spur to improvement."
They include strengthening the vetting and recruitment of staff, establishing a new independent whistleblowing helpline, and a recommitment to report to authorities "any issues that arise that could affect the safety of those we work for or the confidence of the public".
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Mr Goldring, Oxfam chief executive, acknowledged that the charity did not place the full details of allegations in the public domain.
He told Channel 4 News: "I genuinely believe that my predecessors did it to protect the programme of delivering life-saving assistance in Haiti, which would have been massively disrupted had that happened."
He added: "I'm not saying it was the right thing to do, but that was a decision made in good faith at the time.
"What I'm saying now, is that moral leadership now means standing up, apologising, as we have, committing to improve and working with others."
Copyright (c) Press Association Ltd. 2018, All Rights Reserved. Picture (c) BBC / PA Wire.