The claims, which surfaced last week after a report by the Times, have prompted Oxfam's deputy chief executive to resign and have thrown the charity's government funding into question.
Archbishop Emeritus Desmond Tutu has stepped down as an ambassador for Oxfam, citing disappointment at the British aid agency's embroilment in a sex scandal involving staff in Haiti after a massive 2010 natural disaster.
He said: "I am not a saint. I am a man of flesh and blood and I have made mistakes (not easy to admit) and I am DEEPLY ASHAMED", the 68-year-old former soldier wrote in Dutch to broadcaster VTM.
"The allegations appear very serious and we don't rule out the possibility to revoke Oxfam's authorization to operate in Haiti as an NGO, should alleged misconduct prove to be true", he said by phone, late on Tuesday.
He said he had never visited a brothel or nightclub in Haiti and audits had "never shown that funds were used to finance excesses or sex parties".
The charity has admitted to a lack of transparency over an internal investigation about the use of prostitutes by staff in Haiti, who were there to assist the country's recovery after a 2010 quake.
The agency said in a statement it had identified that "one of those dismissed by Oxfam as a result of the sexual misconduct case in Haiti" was "subsequently hired by Oxfam as a consultant in Ethiopia".
There are fears the scandal could hurt funding for the broader global aid sector.
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The aid official at the centre of the Oxfam sex scandal has spoken out for the first time since it was exposed, saying that the revelations were "hard to bear". International Development Secretary Penny Mordaunt said on Wednesday the aid sector needed a change of culture.
The former Haiti country director at the heart of the scandal denied on Thursday that he had paid for sex with prostitutes or abused minors.
In a statement released on Thursday afternoon, the archbishop says he's deeply disappointed by allegations of immorality and possible criminality involving humanitarian workers linked to the charity.
Nobel Peace Prize victor Desmond Tutu has said he will no longer be a global ambassador for Oxfam after allegations that senior staff members in crisis zones paid for sex among the desperate people the group was meant to serve.
"No organisation is too big, or our work with them too complex, for me to hesitate to remove funding from them if we can not trust them to put the beneficiaries of aid first", she said.
"The vast majority of aid workers are good people".
"I expect the European Union to do the same thing I'm asking the United Kingdom government to do: we need to start focusing on prosecuting the bad apples so we can send the message to the predatory paedophiles that the aid industry is no longer a soft target", he said.
"A lot of people, including the global media, will be blushing when they hear my version of the facts".