Oxfam will have funding withdrawn if it fails to comply with authorities over safeguarding issues, the International Development Secretary has warned.
Penny Mordaunt condemned the "horrific behaviour" of some Oxfam staff members and said it was "utterly despicable" that allegations of abuse persisted in the aid sector.
The charity is facing mounting criticism over its handling of allegations of sexual misconduct.
It has denied claims it covered up the use of prostitutes by aid workers in Haiti in 2011 and said it publicly announced an investigation into the claims when they surfaced.
Ms Mordaunt said: "I am writing to all UK charities which receive UK aid, insisting that they spell out the steps they are taking to ensure their safeguarding policies are fully in place and work properly, declare all safeguarding concerns they are aware of, and confirm they have referred all concerns they have about specific cases and individuals to the relevant authorities.
"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 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."
The Charity Commission said on Saturday that it had written to Oxfam "as a matter of urgency" to request further information and "establish greater clarity".
The regulator said an Oxfam report on the investigation stated there had been no allegations of abuse of beneficiaries and made no mention of any potential sexual crimes involving minors.
"Our approach to this matter would have been different had the full details that have been reported been disclosed to us at the time," the Charity Commission said.
Four members of Oxfam staff were dismissed and three, including the country director, resigned before the end of the 2011 investigation.
The charity said allegations that under age girls may have been involved were not proven.
The Department for International Development (DfID) earlier said the allegations raised "serious questions that Oxfam must answer" as it announced a review of its relationship with the charity.
Ms Mordaunt, who has requested talks with Oxfam's senior management "at the earliest opportunity", will also meet the Charity Commission this week to discuss the regulation of UK charities overseas.
She said: "My absolute priority is to keep the world's poorest and most vulnerable people safe from harm.
"In the 21st century, it is utterly despicable that sexual exploitation and abuse continues to exist in the aid sector.
"The horrific behaviour by some members of Oxfam staff in Haiti in 2011 is an example of a wider issue on which DfID is already taking action, both at home and with the international community via the UN."