But it stressed the dismissal of Damien Berrendorf, who served as the Oxfam's country director in Haiti from 2012 to 2017, was "not related to sexual misconduct" and was "not connected to the case in 2011".
In response, Oxfam said it would create a global database of accredited referees to crack down on forged or unreliable references from past or current employees.
He acknowledged having had a brief sexual relationship at his Oxfam house with a local woman whom he met as a result of giving her younger sister milk powder and diapers for her child.
"I'm here for all the women who have been abused, I want them to come forward and for justice to be done for them". In my language 'Okuruga ahamutima gwangye, mutusaasire.' It means "From the bottom of my heart I am asking for forgiveness'".
She said: "The recent revelations about Oxfam - not exclusively the actions perpetrated by a number of those staff - but the way the organisation responded to those events, should be a wake-up call to the sector".
Ms Byanyima added one of her priorities was "to make sure that the work we do at Oxfam, of saving lives, of reaching vulnerable people, continues because it's vital, it must continue".More news: Kerala: CPI(M) leader, six others arrested for assaulting four-month pregnant woman
The Times newspaper reported on Friday (9 February) that some Oxfam staff in Haiti after the country's 2010 quake had paid for sex with prostitutes.
The Department for International Development has been tasked with conducting a new audit of safeguarding arrangements at non-governmental organisations that deliver United Kingdom development aid in the wake of revelations about the conduct of Oxfam staff in Haiti.
The charity has denied a lack of transparency over the Haiti affair, which has prompted a flight of supporters and led the British government to threaten cutting funds to organisations which cover-up sex scandals.
The charity has also lost a number of celebrity ambassadors including Good Will Hunting actress Minnie Driver, and Nobel Peace Prize victor Archbishop Desmond Tutu.
Oxfam faced fresh pressure on Tuesday after a former senior member of staff said her concerns about "a culture of sexual abuse" were not taken seriously by the charity's bosses.
The post comes after actress Minnie Driver became the first celebrity to resign as an Oxfam ambassador in protest at the sex scandal.
Oxfam will triple funding to more than $1 million to address safeguarding processes, while also doubling the number of staff in this area and increasing investment in gender training.