'Our approach to this matter would have been different had the full details that have been reported been disclosed to us at the time, ' it said in a statement.
Thomson announced a package of seven measures on Sunday that she said is created to protect vulnerable people.
The Department for International Development (DFID) said the UK-based charity's leaders had "showed a lack of judgement" in investigating the matter and in its openness with the government and Britain's Charity Commission regulator.
Ms Mordaunt's announcement comes as the Observer reports that Oxfam workers allegedly used prostitutes in Chad in 2006.
A spokeswoman for the Charities Commission said: "In August 2011, Oxfam made a report to the Commission about an ongoing internal investigation into allegations of misconduct by staff members involved in their Haiti programme".
"As a direct result of the stories in The Times, staff members have come forward with concerns about how staff were recruited and vetted in this case", said Caroline Thomson, chair of trustees for Oxfam GB.
The British charity Oxfam is under fire over accusations that some of its aid workers engaged in sexual misconduct in the aftermath of the 2010 quake that devastated Haiti, and that the agency subsequently attempted to cover-up the negligent behavior, according to British officials.
"With hindsight, I would much prefer that we had talked about (the) sexual misconduct", Goldring told BBC radio.
One officer dead, two others shot while serving warrant near Atlanta
Two of the officers were taken from the scene to a hospital by helicopter, while the third was taken to a hospital by ambulance. Price said the police chief and chaplain had spoken with Maddox's wife. "We just can't believe this happened", he said.
"But I don't think it was in anyone's best interest to be describing the details of the behavior in a way that was actually going to draw extreme attention to it when what we wanted to do was get on and deliver an aid program".
She said Oxfam often worked in very hard locations "where the rule of law isn't going on". "We were not told about the nature of these events".
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.
In a statement, Oxfam denied providing positive references for those implicated, and said they were likely provided on an individual capacity.
It said the vast number of aid operations working around the globe meant it was "not possible.to ensure that those found guilty of sexual misconduct were not re-employed in the sector".
Mr Goldring told the charity did "anything but" cover the incident up, adding: "We were very open with the public that we were ashamed of the behaviour of our staff".
But the charity said it had publicly announced an investigation into the allegations when they surfaced in 2011.
Oxfam said it now had a dedicated safeguarding team, a confidential whistleblowing hotline and safeguarding contact point within countries, and a code of conduct that stipulated: "I will also not exchange money, offers of employment, employment, goods or services for sex or sexual favours".