Tutu was also saddened that the allegations would tarnish the good work achieved by many thousands of people working for Oxfam, it added.
The atmosphere of chaos swirling around Oxfam also deepened as the organisation admitted a "serious error" in rehiring one of those accused of sexual misconduct as a consultant in Ethiopia.
"Hiring him, even in an emergency as a short-term consultant, was a serious error and should never have happened", a statement said.
He said he resigned his post running the Oxfam operation after the 2010 Haiti quake because he had failed to exercise sufficient control over staff accused of sexual misconduct.
"The Archbishop is deeply disappointed by allegations of immorality and possible criminality involving humanitarian workers linked to the charity", said a statement from his office in South Africa".
"Parties every week? Chic villas?"
It was reported last week that some Oxfam staff paid for sex with prostitutes in Haiti while in the country after the devastating 2010 quake.
"A lot of people, including the global media, will be blushing when they hear my version of the facts".
Senior staff have already left the charity.
He was then hired by Oxfam as a country director in Chad.
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.
In an open letter to Belgian media (in Dutch), Mr Van Hauwermeiren said he had resigned for failing to control rumours about sex scandals involving Oxfam in Haiti and for "feeding the rumours" through his own relationship with a Haitian woman.
"As soon as the allegations were reported via Oxfam's whistleblowing line, they were investigated and the individual was dismissed".
The former aid worker said that he meant to release a statement...
A new unit dedicated to reviewing safeguarding in the aid sector and stopping "criminal and predatory individuals" being employed by other charities has been created, and a global register of development workers may be established.