In an Instagram post, the activist, who is married to actor Colin Firth, said she was no longer an active ambassador for the charity.
But she said her name remained on the charity’s website because she “wanted to show gratitude and support for what they try to do”.
Her comments follow claims that some of Oxfam’s aid workers used prostitutes in Haiti following the 2010 earthquake.
Firth wrote: “It is appalling to hear the news of the men that have abused the people they were there to help.
“It’s a betrayal of all who put their faith in them: those who most needed their help. Also, those who supported them in good faith. The failure to deal with it adequately has further undermined that trust.”
However, Firth said it would be a “tragedy” if the charity’s work came to a halt.
“I still believe that such programmes are necessary. It would be a tragedy to see this relief work and advocacy stopped,” she said.
“For its part Oxfam must address this abuse diligently and transparently. Oxfam must do everything in its power to heal the damage to those who depend on both its work and the good faith and generosity of its supporters.”
A post shared by Livia Firth (@liviafirth) on Feb 14, 2018 at 10:51am PST
The Italian director said she first travelled with the charity in 1997 to Ethiopia and had been “inspired” by aid workers’ “passion, courage, integrity and compassion”.
Firth added: “What they were doing struck me as difficult, but vitally important work. I could see that they gave scrupulous thought to how to help and empower the world’s most vulnerable people.”
The post comes after actress Minnie Driver became the first celebrity to resign as an Oxfam ambassador in protest at the sex scandal.
She said she was “horrified” by the allegations.
On Wednesday, International Development Secretary Penny Mordaunt said she would meet the National Crime Agency on Thursday following a week of talks with charity bosses, regulators and experts.
She said Oxfam had failed to show “moral leadership” and properly inform donors, regulators and prosecutors of the allegations.
Ms Mordaunt added: “No organisation is too big, or our work with them too complex, for me to hesitate to remove funding from them if we cannot trust them to put the beneficiaries of aid first.”
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.
Oxfam later confirmed it sacked its country director in Haiti last year following allegations of “mismanagement” and “inappropriate behaviour”.
More from Oxfam
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Oxfam ‘gave us no details about ex-worker who admitted using prostitutes’, says other charity
Minnie Driver quits Oxfam ambassador role over charity’s sex scandal
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Damien Berrendorf, who served as Oxfam’s country director in Haiti from 2012 to 2017, was dismissed after the allegations were reported through the charity’s own whistleblowing line.
The charity insisted Mr Berrendorf’s dismissal was “not connected to the case in 2011” and “not related to sexual misconduct”.