She also set up a new unit in her ministry to ensure all aid recipients are safeguarded from harm.
Oxfam's chief executive Mark Goldring has said he will not stand down unless the charity's board tells him it has lost faith in his leadership, and has apologised to Ms Evans over the way her concerns were handled.
Oxfam chair of trustees, Caroline Thomson, said in response to the statement by DfID: "Oxfam is in total agreement with the secretary of state's further proposals".
Evans told Channel 4 News of a survey conducted during her 2012-2015 tenure which exposed a "culture of sexual abuse" in some Oxfam offices.
But she added: We're going to move on and, I hope, continue to earn... the support of the British public.
One of the best-known worldwide NGOs, with aid programs running across the globe, Oxfam was under threat of losing its British government funding over sexual misconduct allegations first reported by the Times newspaper last week.
It was revealed that one of the persons accused of sexual misconduct later began working for CAFOD in the Philippines, after leaving Oxfam.
"We've made very clear that had the details of what has come out over the last few days been told to us, we would have dealt with this very differently", said Michelle Russell, the Charity Commission's director of investigations.
She also detailed concerns about abuse of staff as young as 14 in Oxfam shops.
She said a meeting was held to discuss her concerns about widespread abuse but no action was taken until past year. I asked repeatedly: we need more resource for this and it wasn't forthcoming.
The former Richmond MP also knows that the continuing lurid claims about the sexual exploitation of the most vulnerable, the victims that the charities were supposedly helping, will make it harder to justify the £13bn a year that Britain now spends in this field when domestic policy priorities are denied funds.
The devastating 2010 quake in Haiti killed more than 200,000 people and caused damage worth an estimated 117 percent of GDP in the already impoverished nation, the poorest in the Americas.
Haitian President Jovenal Moise also waded into the scandal for the first time late Monday, when he posted on Twitter that the abuse in his country was a "extremely serious violation of human dignity".
Miss Mordaunt has sent a letter all United Kingdom charities working overseas - including Oxfam - to demand they do more "to fully protect vulnerable people".
Aid minister Penny Mordaunt, who threatened on Sunday to withdraw government funding from Oxfam unless it gave the full facts about events in Haiti, summoned senior managers from the charity to a meeting on Monday.
British officials said Oxfam is risking $60 million in annual government funding over a lack of transparency in dealing with the alleged misconduct.
Former global development secretary Justine Greening has said she does not recall being aware of allegations surrounding Oxfam workers in Haiti.
After the interview aired, Evans tweeted a statement summarising her position.
Helen Evans, the charity's former safeguarding chief for six years, said that 286 allegations of sexual exploitation and abuse were reported by Oxfam over the past nine years.
Oxfam has apologized unreservedly, but denied that it attempted to cover up the scandal.