In a further warning to the charity, she said: 'If they do not hand over all the information that they have from their investigation and subsequently to the relevant authorities, including the Charity Commission and prosecuting authorities, then I can not work with them any more as an aid delivery partner'.
Oxfam workers were accused of paying Haitian natural disaster survivors for sex during relief efforts.
The Charity Commission took no further action at the time but says it would have acted differently had it known all the facts.
She admitted she was considering whether the organisation should receive any more funding from the Department for International Development - which gave it £32m in the last financial year.
The charity's chief executive Paul Goldring will meet Penny Mordaunt, the worldwide development secretary, on Monday after she threatened to withdraw millions of pounds of government funding.
Oxfam said four members of staff were dismissed and three, including the country director, were allowed to resign before the end of the investigation.
"I think it is a complete betrayal of both the people that Oxfam were there to help, and also the people that sent them there to do that job - it's a scandal", she said. "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.
Former Oxfam employees in Chad claimed staff held sex parties with prostitutes.More news: LeBron James Has Message For Buddy Dwyane Wade After Cavs-Heat Trade
"I have so much respect for Oxfam, they do great work, but this is a sector wide problem", the former staffer told the Observer.
Oxfam said it could not corroborate the latest claims but it said it was "shocked and dismayed" at what it called the unacceptable behaviour by a small number of people.
Oxfam will examine new complaints from staff members about how the aid workers involved in 2010 were recruited and vetted.
Among the alleged misconduct is paying sex workers and sexual abuse.
Ms Thomson said she was working closely with chief executive Mark Goldring to make improvements.
The British government is reviewing its relationship with Oxfam amid a deepening sexual misconduct scandal involving some of the charity's employees working in Haiti after its devastating 2010 natural disaster.
Marr said: 'That was a lie, wasn't it?'
And it will extend an existing review into bad behaviour and the charity's culture to include looking at how people are hired and managing of staff in challenging environments. "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 also be meeting with Oxfam's representatives on Monday, adding: "I'm very clear it doesn't matter whether you've got a whistle-blowing hotline, it doesn't matter if you've got good safeguarding practices in place".