Oxfam has agreed to stop bidding for Government funding until ministers are satisfied it can meet the "high standards" expected.
International Development Secretary Penny Mordaunt said the charity had agreed not to bid for taxpayers' money amid allegations some of Oxfam's aid workers used prostitutes in Haiti following the 2010 earthquake.
She said the Government would take "whatever decisions about past or future funding" to the charity or others "that we deem necessary".
The minister's statement follows the charity's response to demands outlined by Ms Mordaunt on Monday.
"I made three demands: that they make clear how they will handle any forthcoming allegations around safeguarding – historic or live; that they report staff members involved in this incident to their respective national governments; and that they fully co-operate with the Haitian authorities, including handing over all evidence they hold," she said.
"Oxfam has now confirmed that they have complied with all of these points.
"Following our discussions, Oxfam has agreed to withdraw from bidding for any new UK Government funding until DfID (Department for International Development) is satisfied that they can meet the high standards we expect of our partners."
The Government spent £13.4bn on foreign aid last year, which is 0.7% of GDP. That figure includes almost £31.7m for Oxfam.
The charity also relies heavily on public donations, with £115m of its total income coming from donations, legacies and a Disasters Emergency Committee appeal. Retail sales contributed more than £90m.
Ms Mordaunt said her priority was to "deliver for the world's poorest and most vulnerable" and keep people "safe from harm".
She added: "We have asked for assurances from all our charitable partners regarding their safeguarding and reporting practices by 26 February, including Oxfam.
"At that stage we will make further decisions about continuing or amending how those programmes are delivered.
"We have been very clear that we will not work with any organisation that does not live up to the high standards on safeguarding and protection that we require."
The politician said the "hundreds of good, brave and compassionate" Oxfam workers had been "poorly served by Oxfam's leadership".
"Clearly Oxfam have a long way to go before they can regain the trust of the British public, their staff and the people they aim to help," Ms Mordaunt said. "The actions and attitude of the organisation over the coming weeks will be critical.
"I am determined that we do our utmost to prevent exploitation and abuse happening – and ensure that where it does happen it is identified and dealt with appropriately."
She then called on the aid sector to "step up" and "demonstrate the leadership required".
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Following the allegations coming to light, Oxfam issued an "unreserved apology" to the Government, donors, supporters and the people of Haiti over its handling of the claims.