Ministers could cut off funding for Oxfam if it cannot account for the way it handled claims of sexual misconduct by aid workers, the international development secretary has warned.
Penny Mordaunt will meet the charity on Monday to hear more about claims staff used prostitutes in Haiti in 2011.
She said Oxfam had failed in its "moral leadership" over the "scandal".
Meanwhile, Oxfam has announced new measures for the prevention and handling of sexual abuse cases.
Ms Mordaunt told the BBC's Andrew Marr she had written to other organisations funded by Department for International Development (DfID) urging them to report any safeguarding issues, past or present, and pledged they would all be followed up.
Oxfam has faced growing criticism for the way it handled the allegations of misconduct by its staff in Haiti, where they were working in the aftermath of the huge earthquake that devastated they country in 2010.
The charity's own investigation into the allegations led to four people being sacked and three others resigning - among them its country director, Roland van Hauwermeiren.
Ms Mordaunt said the allegations were "a complete betrayal of both the people Oxfam were there to help and also the people that sent them there to do that job".
She said Oxfam did "absolutely the wrong thing" by not reporting the detail of the allegations and that no organisation could be a government partner if it did not "have the moral leadership to do the right thing".
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She said she was considering whether Oxfam should receive any more funding from the government - which gave it £32m ($44m) in the last financial year.
Oxfam's chairman of trustees, Caroline Thomson, said the reports in the Times newspaper had led to other staff coming forward with concerns about how employees were recruited and vetted.
She said the charity's board had appointed a consultant earlier this year to review its culture and working practices, which would now be extended.
"If that review brings about a safer environment for all, then the publicity of the last few days, painful as it has been, will also have been valuable," she said.
"It is not sufficient to be appalled by the behaviour of our former staff - we must and will learn from it and use it as a spur to improvement."
The charity will also introduce tougher vetting of staff and mandatory safeguarding training for new recruits and work with the rest of the aid sector to make it easier to share intelligence about people who have been found guilty of sexual misconduct.
This will be in addition to measures designed to prevent sexual abuse and misconduct and improve the handling of allegations which Oxfam says it introduced in the wake of the Haiti case in 2011.
Meanwhile, Oxfam is facing further allegations, reported in the Observer, that staff on its mission in Chad - also led by Mr van Hauwermeiren - used prostitutes in 2006.
Oxfam said it could not corroborate the latest claims.
The Sunday Times has also reported new allegations, saying more than 120 workers from UK charities were accused of sexual abuse in the past year.
Ms Mordaunt's predecessor Priti Patel said she was aware of a wider issue of sexual abuse and child exploitation from when she was at DfID.
She told Radio 5 live's Pienaar's Politics there was "a culture of denial in the aid sector about the exploitation and sexual abuse that has taken place historically for decades" and called for a database for "predatory paedophiles" who she claimed could be infiltrating the organisations.
Ms Mordaunt said she suspected there were paedophiles targeting the sector to carry out predatory activities, making it important that aid organisations reported offences.
What happened when?
The allegations of misconduct by Oxfam staff in Haiti date from 2011 but came to light in a report in the Times on Friday, which said the charity's country director for Haiti, Roland Van Hauwermeiren, was alleged to have used prostitutes at a villa rented for him by Oxfam in the aftermath of the 2010 earthquake.
Oxfam knew about the allegations at the time and launched an internal investigation, as a result of which four members of staff were dismissed.
Three others, including Mr Van Hauwermeiren, were allowed to resign before the end of the investigation.
Mr Van Hauwermeiren went on to work elsewhere in the sector, but Oxfam said it would not have provided a positive reference.
The charity says it made a report public at the time which said "serious misconduct" had taken place in Haiti and issued a press release - but did not give details of the allegations.
It told the Charity Commission it was investigating inappropriate sexual behaviour, bullying, harassment and staff intimidation but did again not reveal the exact details.
The regulator took no further action at the time, but has since said it would have acted differently had it known all the facts.
Oxfam has denied any cover-up.
Its chief executive, Mark Goldring, told the BBC that describing details of the behaviour at the time could have drawn "extreme attention" to it, which he said would have been in no-one's best interest.