Video report by ITV News Political Correspondent Daniel Hewitt
Funding will be withdrawn from Oxfam if it does not comply fully with authorities following allegations of sexual misconduct.
International Development Secretary Penny Mordaunt criticised the "horrific behaviour" of some staff members after aid workers were said to have used prostitutes in the wake of the 2010 Haiti earthquake.
Oxfam has found itself under fire over allegations the charity tried covering the accusations up.
Ms Mordaunt has now warned Oxfam and other charities that funding will be stopped if safeguarding policies are not in place.
"With regard to Oxfam and any other organisation that has safeguarding issues, we expect them to cooperate fully with such authorities, and we will cease to fund any organisation that does not," she said on Sunday.
Ms Mordaunt added: "I am very clear: we will not work with any organisation that does not live up to the high standards on safeguarding and protection that we require."
She also told The Andrew Marr Show Oxfam had "failed" in its moral leadership by allowing accused staff - who she said had "betrayed" the charity - to resign and not pass on relevant information to the authorities.
The Charity Commission said that it had written to Oxfam "as a matter of urgency" to request further information and "establish greater clarity".
In response the charity has announced a package of new measures to "strengthen the prevention and handling of sexual abuse cases".
Caroline Thomson, Oxfam's GB chair of trustees, said in a statement that she shared "the anger and shame" the reports had generated.
"It is clear that such behaviour is completely outside our values and should never be tolerated," she said.
Ms Thomson added: "We apologise unreservedly. We have made big improvements since 2011 and today I commit that we will improve further."
Oxfam said it would bolster its safeguarding policies including through the introduction of an independent consultant to help "drive out unacceptable behaviour".
Oxfam CEO 'deeply ashamed'
On Saturday Oxfam's CEO told ITV News he was sorry for the incident but denied it had been covered up.
"I am deeply ashamed about Oxfam's behaviour then," Mark Goldring said.
"Everybody, the 25,000 staff and volunteers are compromised by this.
"The hundreds of thousands of people that support Oxfam every month are compromised by this, and to everybody I do apologise."
The charity said it had publicly announced an investigation into the allegations when they surfaced seven years ago.
But the charity regulator said Oxfam's report stated there had been no allegations of abuse of beneficiaries and did not mention potential sexual crimes involving minors.
Four members of staff were dismissed and three, including the country director, resigned before the end of the 2011 investigation, Oxfam said.
"Oxfam had no formal obligation to anybody anything, this wasn't a public story, this was an internal investigation," Mr Goldring said.
He said if he were in the role at the time he would have said more about the incident.
"I think we should have been open that there was sexual misconduct and that involved the use of prostitutes," he said.
Mr Golding said it would have been "highly likely" donations to Oxfam would have dropped if the incident had come to light during the investigation.
Select Committee's Paul Scully questions Oxfam transparency
The government review comes amid reports in The Times that Oxfam did not tell other aid agencies about the behaviour of staff involved in the investigation after they left to work elsewhere.
Paul Scully, a member of the International Development Select Committee, said that concerns around reputation was a "disincentive" for charities to be transparent.
"The fact that the government are taking on this investigation and the charity commission are looking at it themselves shows that probably not enough was done at the time," he told ITV News.
"We are absolutely right to investigate and look at exactly what happened and make sure it never happens again."
Mr Scully added: "DfID works with a lot of big multi-national companies and charities and there is then a reputational issue.
"So there is a sort of disincentive in the system to mean they are maybe not as transparent as they might be with this sort of information."
DfID said Oxfam had "serious questions" to answer following the revelations.
A DfID spokesman said: "We often work with organisations in chaotic and difficult circumstances.
"If wrongdoing, abuse, fraud, or criminal activity occur we need to know about it immediately, in full."