Save The Children said all 31 abuse allegations took place in foreign countries and that 16 people had been dismissed as a result.
Thompson said she shared the "anger and shame that behavior like that highlighted in Haiti in 2011 happened in our organization".
Oxfam will examine new complaints from staff members about how the aid workers involved in 2010 were recruited and vetted.
The newspaper said Roland van Hauwermeiren, who later worked in post-earthquake Haiti, was head of Oxfam's operations in Chad at the time.
The worldwide development secretary has said the government will end funding to Oxfam unless the charity shows "moral leadership" and hands over all its information on its aid workers' apparent use of prostitutes in Haiti.
Mr Goldring's words come after the Department for International Development said late Friday that the charity had shown a "lack of judgement" in its investigations following the 2010/11 incidents.
The British Red Cross admitted there had been a "small number of cases of harrasment reported in the UK", believed to be as many as five.
The charity said it launched an immediate investigation in 2011 which found a "culture of impunity" among some staff but has denied trying to cover up the scandal.
Champagne orders review of controversial helicopter deal with the Philippines
He admitted that the government was buying helicopters precisely to advance the government's operations against local insurgents. The allegations relate to extrajudicial executions committed during the president's war on drugs, which has killed thousands.
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".
Goldring apologised yesterday and said he was 'deeply ashamed of Oxfam's behaviour [in Haiti]'. The charity allowed staff members to resign from the organisation and seek new aid jobs elsewhere.
She told the BBC's Andrew Marr Show: I am affording them the opportunity to tell me in person what they did after these events and I'm going to be looking to see if they are displaying the moral leadership that I think they need to now.
She will also seek to confirm they have referred all concerns about specific cases and individuals to the relevant authorities.
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 cannot have you as a partner'.
Ms Mordaunt called the behaviour utterly despicable and threatened to cut the charity off from Government funding if she was unsatisfied with answers from an upcoming meeting on Monday. "What is so disturbing about Oxfam is that when this was reported to them, they completely failed to do the right thing", she said.
Mordaunt said she would write to British charities working overseas demanding they declare any problems relating to the duty they have to protect their staff and the people they work with from harm and abuse - so-called "safeguarding".
The charity should immediately hand over its entire 2011 investigation into the sexual misconduct to the appropriate prosecuting authorities and the Charity Commission, she said.