"I told Oxfam they must now demonstrate the moral leadership necessary to address this scandal, rebuild the trust of the British public, their staff and the people they aim to help, and deliver progress on these assurances," she added in a statement.
The statement did not address the question of funding. There was no immediate comment from Oxfam.
The Times newspaper reported on Friday that some staff who were in Haiti after the 2010 earthquake there had paid for sex with prostitutes. Oxfam has neither confirmed nor denied that specific allegation but has said an internal investigation in 2011 had confirmed sexual misconduct had occurred.
Announcing her resignation on Monday, deputy CEO Penny Lawrence said Oxfam had become aware over the past few days that concerns were raised about the behaviour of staff in Chad as well as Haiti that the organisation failed to adequately act upon.
"It is now clear that these allegations, involving the use of prostitutes and which related to behaviour of both the country director and members of his team in Chad, were raised before he moved to Haiti," she said.
"As programme director at the time, I am ashamed that this happened on my watch and I take full responsibility."
Oxfam has said that as a result of its internal investigation in 2011, four people were dismissed, and three others, including the Haiti country director who had previously held the same role in Chad, had resigned.
In its last financial year Oxfam received GBP32 million ($61 million) from Britain's aid ministry, about 8 per cent of its overall income. Whether or not it loses that funding, private donations could be hit by the bad publicity.