The apology comes as the Department of global development, which previous year gave Oxfam more than £30 million, said it will review whether or not to continue to fund the charity.
Worldwide development secretary Penny Mordaunt said it was "despicable" that sexual exploitation and abuse existed in the aid sector and threatened to cut funding to charities if they fail to comply with authorities over safeguarding issues.
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.
Former Oxfam staff in Chad told the paper that "women believed to be prostitutes were repeatedly invited to the Oxfam team house there", and a senior staff member was sacked for his behaviour in 2006.
Ms Mordaunt told BBC1's The Andrew Marr Show that the failure to pass on information to relevant authorities shows an "absolute absence of leadership".
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Although the charity has denied covering up the alleged scandal, Christian Aid said the claims are "deplorable".
Ms Mordaunt announced she would meet the charity on Monday to discuss the case, and said: "If the moral leadership at the top of the organisation is not there then we can not have you as a partner".
Thomson announced a package of seven measures on Sunday that she said is created to protect vulnerable people. I made this our own agenda, I did my research, this [sexual abuse] is well-documented.
Her department had not been told in 2011 about the nature of the events reported to have taken place in Haiti, although some details were disclosed to the charities regulator, she added.
Oxfam said it had no report of the Chad allegations, but had introduced steps to prevent sexual exploitation of the vulnerable people they deal with after the Haiti revelations.
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He added: "Everybody - the 25,000 staff and volunteers - are compromised by this, the hundreds of thousands of people who support Oxfam every month are compromised by this, and to everybody I apologise".
Penny Mordaunt said it was "despicable" that sexual exploitation and abuse still existed in the aid sector.
The Times of London, which first exposed the scandal, has reported that several of the aid workers dismissed by Oxfam for inappropriate behavior found work with other aid agencies.
On Sunday, Mordaunt said she did not think new procedures alone would be enough to convince her that Oxfam should continue to receive public funds.
Oxfam has denied allegations that it tried to hide that some of its staff paid prostitutes in the aftermath of the natural disaster.
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To date, four employees were fired from their posts and another three resigned before the investigation was complete.
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