The country's charity regulator, the Charity Commission, said Oxfam had a duty to protect its staff and the people they work with - a process known as "safeguarding" - and had to declare any problems it had.
"If they do not hand over all the information they have from their investigation subsequently to the relevant authorities including the Charity Commission and prosecuting authorities, then I can not work with them any more".
Late on Friday, the Department for International Development (DFID) also said it was reviewing its relationship with the UK-based charity, to which it gave almost £32 million (36 million euros/$44 million) past year.
Mordaunt says there was a failure of "moral leadership" at Oxfam.
The charity said allegations that under-age girls may have been involved were not proven.
It is a "complete betrayal of both the people Oxfam were there to help and also the people that sent them there to do that job", Britain's worldwide development secretary, Penny Mordaunt, told BBC News, which noted that the nonprofit received $44 million in government funds a year ago.
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"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.
'We also want to satisfy ourselves that we do now have a culture of openness and transparency and that we fully learn the lessons of events in 2011'.
Oxfam has been at the centre of a firestorm of controversy after it was revealed that Oxfam staff had paid for sex whilst working in Haiti.
The government's hardening stance follows reports in The Times newspaper that young sex workers were hired by Oxfam's senior staff in Haiti after the 2010 natural disaster which devastated the island and left up to 300,000 people dead.
The source added staff members did not speak up for fear this might reduce donations to the most vulnerable at a time when funding is under pressure.
Oxfam said it was "shocked and dismayed" by the new Chad claims.
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The United Kingdom's Department for International Development sharply criticized the charity for its lack of transparency as questions swirled about how much detail Oxfam provided when it first reported the allegations.
The British Red Cross said a "small number of cases of harassment" had been reported in the UK. It said significant improvements have already been made since 2011.
Charities, including Oxfam, have been told they will have funding withdrawn if they fail to comply with authorities over safeguarding issues.
Goldring apologised yesterday and said he was 'deeply ashamed of Oxfam's behaviour [in Haiti]'. The charity employs 5,000 staff and has a further 23,000 volunteers.
Oxfam's chairwoman of United Kingdom trustees, Caroline Thomson, said it was working to "address the underlying cultural issues that allowed this behaviour to happen".
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". However, the minister said Oxfam did "absolutely the wrong thing" by not reporting the detail of the incidents to the government.
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