Oxfam lied and failed in its “moral leadership” in the wake of allegations of sexual misconduct by aid workers, the International Development Secretary has said.

Penny Mordaunt condemned the behaviour of some Oxfam staff members as a “complete betrayal”, as she warned the charity the “scandal” had put its relationship with the Government at risk.

Oxfam is facing mounting criticism over its handling of sex allegations, but has denied it tried to cover up the use of prostitutes by workers in Haiti in 2011.

Ms Mordaunt told BBC1’s The Andrew Marr Show that the failure to pass on information to relevant authorities shows an “absolute absence of leadership”.

Asked by Marr if she thought Oxfam had failed in its “moral leadership”, the Conservative MP replied: “Yes, I do.”

Ms Mordaunt announced she would meet the charity on Monday to discuss the case, and said: “If the moral leadership at the top of the organisation is not there then we can not have you as a partner.”

Charities, including Oxfam, have been told they will have funding withdrawn if they fail to comply with authorities over safeguarding issues.

The Charity Commission said on Saturday that it had written to Oxfam “as a matter of urgency” to request further information.

The regulator said an Oxfam report on the investigation stated there had been no allegations of abuse of beneficiaries and made no mention of any potential sexual crimes involving minors.

“Our approach to this matter would have been different had the full details that have been reported been disclosed to us at the time,” it said in a statement.

Ms Mordaunt said the charity had also “categorically” stated to the Department for International Development (DfID) that no harm was done and beneficiaries were not involved.

Marr said: “That was a lie, wasn’t it?”

Ms Mordaunt replied: “Well, quite.”

She added that Oxfam had done “absolutely the wrong thing” by failing to inform authorities about the full details of the allegations.

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 cannot work with them any more as an aid delivery partner.”

Four members of Oxfam staff were dismissed and three, including the country director, resigned before the end of the 2011 investigation.

The charity said allegations that under-age girls may have been involved were not proven.

Ms Mordaunt has written to all UK charities which receive UK aid urging them to declare any safeguarding issues, and will also meet the Charity Commission this week to discuss the regulation of organisations overseas.

Former International Secretary Priti Patel said there was a “culture of denial” in the aid sector about exploitation.

She told BBC Radio 5 Live’s Pienaar’s Politics she was not aware of allegations within Oxfam, but had raised the issue of abuse involving aid workers in disaster zones with DfID while heading the department.

“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 said.

“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.”