According to The Observer, women were repeatedly invited "for parties" at Oxfam's team premises.
A lot of people knew about this, she told Sky News, naming the Charity Commission and DFID (Department for International Development).
Mordaunt called Oxfam's behavior "utterly despicable" and said the agency was suffering from a failure of "moral leadership".
Oxfam said it had not found evidence to back one of the Times' most explosive claims: that underage girls were involved.
Worldwide development secretary Penny Mordaunt said it was "despicable" that sexual exploitation and abuse existed in the aid sector and threatened to cut funding to charities if they fail to comply with authorities over safeguarding issues.
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In its statement, Oxfam said it had informed its trustees, the government, as well as other major donors such as the European Union, the World Health Organization and other United Nations agencies of the investigation and the outcome.
"With hindsight, I would much prefer that we had talked about (the) sexual misconduct", Goldring told BBC radio.
Roland van Hauwermeiren, who resigned from Oxfam in 2011 after admitting that prostitutes had visited his villa in Haiti, was head of Oxfam in Chad at the time.
The government's hardening stance follows reports in The Times newspaper that young sex workers were hired by Oxfam's senior staff in Haiti after the 2010 quake which devastated the island and left up to 300,000 people dead.
Everybody - the 25,000 staff and volunteers - are compromised by this, the hundreds of thousands of people who support Oxfam every month are compromised by this, and to everybody I apologise, he said. The charity had a fund worth more than $100 million to provide relief supplies and help rebuild Haiti's infrastructure, the Times reported.
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.
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There are no details on how ZioShiba got the iBoot source code, but after seeing it, we're certain it's the real deal . He even confirmed that the boot is legitimate, because it seems to align with the code he himself reverse-engineered.
Although the charity has denied covering up the alleged scandal, Christian Aid said the claims are "deplorable".
And it will extend an existing review into bad behaviour and the charity's culture to include looking at how people are hired and managing of staff in challenging environments.
Oxfam chief executive Mark Goldring apologised on Saturday, saying he was deeply ashamed of Oxfam's behaviour.
Marr said: 'That was a lie, wasn't it?' However, the minister said Oxfam did "absolutely the wrong thing" by not reporting the detail of the incidents to the government.
However, Mordaunt said not disclosing the full picture was "a scandal" and Monday's meeting was a chance "to see if they are displaying the moral leadership that I think they need to now".
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